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19

Jun 28, 2018
06/18

by
Robert Ralowski; Szymon Zeberski

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In this paper we consider nonmeasurablity with respect to sigma-ideals defined be trees. First classical example of such ideal is Marczewski ideal s_0. We will consider also ideal l_0 defined by Laver trees and m_0 defined by Miller trees. With the mentioned ideals one can consider s, l and m-measurablility. We have shown that there exists a subset A of the Baire space which is s, l and m nonmeasurable at the same time. Moreover, A forms m.a.d. family which is also dominating. We show some...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1507.02496

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13

Jun 28, 2018
06/18

by
Olena Karlova

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We investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\to\mathbb R$ which is not Baire measurable. We show that if $X$ is a product of normed spaces $X_n$, $a\in X$ and $\sigma(a)=\{x\in X:|\{n\in\mathbb N: x_n\ne a_n\}|

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1508.01366

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4.0

Jun 30, 2018
06/18

by
Leandro F. Aurichi; Lyubomyr Zdomskyy

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We present an internal characterization for the productively Lindel\"of property, thus answering a long-standing problem attributed to Tamano. We also present some results about the relation Alster spaces vs. productively Lindel\"of spaces.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1704.03843

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4.0

Jun 28, 2018
06/18

by
V. V. Mykhaylyuk

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We introduce a class of $\beta-v$-unfavorable spaces, which contains some known classes of $\beta$-unfavorable spaces for topological games of Choquet type. It is proved that every $\beta-v$-unfavorable space $X$ is a Namioka space, that is for any compact space $Y$ and any separately continuous function $f:X\times Y\to \mathbb R$ there exists a dense in $X$ $G_{\delta}$-set $A\subseteq X$ such that $f$ is jointly continuous at each point of $A\times Y$.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1512.07474

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4.0

Jun 29, 2018
06/18

by
V. V. Mykhaylyuk

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It is shown that for any Baire space $X$, linearly ordered compact $Y$ and separately continuous mapping $f:X\times Y\to\mathbb R$ there exists a dense in $X$ $G_\delta$-set $A\subseteq X$ such that $f$ is jointly continuous at every point of $A\times Y$, i.e. any linearly ordered compact is a co-Namioka space.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1601.06488

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24

Jun 29, 2018
06/18

by
Alexander V. Osipov; Evgenii G. Pytkeev

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In this paper, we give necessary and sufficient conditions for the space B_1(X) of first Baire class functions on a Tychonoff space X, with pointwise topology, to be (strongly) sequentially separable.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1604.05116

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3.0

Jun 30, 2018
06/18

by
Marek Cuth

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We prove that a compact space is monotonically Sokolov if and only if it is monotonically $\omega$-monolithic. This gives answers to several questions of R. Rojas-Hernandez and V. V. Tkachuk.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1401.7501

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4.0

Jun 30, 2018
06/18

by
René Bartsch

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Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in theoretical computer sciences, for example (to illustrate the wide scope of this concept). Moreover, there are many connections between hyperspaces and function spaces in topology. Thus results from hyperspaces help to get new results in function spaces and...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1410.3137

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5.0

Jun 29, 2018
06/18

by
F. Casarrubias-Segura; S. García-Ferreira; R. Rojas-Hernández

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We give a new characterization of Valdivia compact spaces: A compact space is Valdivia if and only if it has a dense commutatively monotonically retractable subspace. This result solves Problem 5.12 from \cite{sal-rey}. Besides, we introduce the notion of full $c$-skeleton and prove that a compact space is Corson if and only if it has a full $c$-skeleton.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1607.00297

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4.0

Jun 30, 2018
06/18

by
Serkan Atmaca; İdris Zorlutuna

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In this paper, we introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated basic properties of it. We study the closure, interior, base, continuity and compactness and properties of these concepts in fuzzy parametrized soft topological spaces

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1401.3119

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3.0

Jun 30, 2018
06/18

by
Menachem Shlossberg

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We study Graev ultra-metrics which were introduced by Gao. We show that the free non-archimedean balanced topological group defined over an ultra-metric space is metrizable by a Graev ultra-metric. We prove that the Graev ultra-metric has a maximal property. Using this property, among others, we show that the Graev ultra-metric associated with an ultra-metric space $(X,d)$ with diameter$\leq 1$ coincides with the ultra-metric $\hat{d}$ of Savchenko and Zarichnyi.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1405.2244

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3.0

Jun 28, 2018
06/18

by
Jacek Kucab; Michael Zarichnyi

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Using a result of Dranishnikov and Smith we prove that, under some conditions, the asymptotic power dimension of a proper metric space coincides with the dimension of its subpower corona.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1512.07739

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4.0

Jun 29, 2018
06/18

by
Sergey Medvedev

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It is proved that for an h-homogeneous space X the following conditions are equivalent: 1) X is a densely homogeneous space with a dense complete subspace; 2) X is $\sigma$-discretely controlled.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1601.03798

3
3.0

Jun 29, 2018
06/18

by
Steven Clontz; Scott Varagona

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A relation $f\subseteq X^2$ satisfies condition $\Gamma$ if there exist distinct $x,y\in X$ with $\langle x,x\rangle ,\langle x,y\rangle ,\langle y,y\rangle \in f$. The authors improve a previous result by characterizing nontrivial idempotent bonding relations on compact Hausdorff spaces as those satisfying condition $\Gamma$.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1603.06162

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4.0

Jun 29, 2018
06/18

by
Eiichi Matsuhashi; Vesko Valov

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We introduce the notion of set-wise injective maps and provide results about fiber embeddings. Our results improve some previous results in this area.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1605.04496

3
3.0

Jun 29, 2018
06/18

by
Robert Bonnet; Arkady Leiderman

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A topological space $L$ is called a linear ordered topological space (LOTS) whenever there is a linear order $\leq$ on $L$ such that the topology on $L$ is generated by the open sets of the form $(a, b)$ with $a < b$ and $a, b \in L \cup \{ -\infty, +\infty \}$. A topological space $X$ is called a generalized ordered space (GO-space) whenever $X$ is topologically embeddable in a LOTS. Main Theorem: Let $X$ be a Hausdorff topological space. Assume that any continuous image of $X$ is a...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1605.05271

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3.0

Jun 28, 2018
06/18

by
Yeorgios Dossidis

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In the papers from Chui and Parnes (1971) and Luh (1972), as well on the paper from V.Nestoridis (1996) on the Universal Taylor series, it is used, without proof, that the union of two compact sets in $\mathbb{R} ^2$ with connected complement has a connected complement. In this work we present a rigorous proof of this fact, by studying some important topological properties of the plane.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1512.04717

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4.0

Jun 30, 2018
06/18

by
Li Chen

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This paper gives a concise proof of the Jordan curve theorem on discrete surfaces. We also embed the discrete surface in the 2D plane to prove the original version of the Jordan curve theorem. This paper is a simple version of L. Chen, Note on the discrete Jordan curve theorem (revised version), arXiv:1312.0316. We seek to clarify and simplify some statements and proofs. Again, the purpose of this paper is to make the proof of the theorems easier to understand. In this revision, we added...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1411.4621

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5.0

Jun 30, 2018
06/18

by
Federico Cantero

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We prove that the inclusion of map(X,Y) into map(K(X),K(Y)) is continuous, where K(X) is the space of non-empty compact subsets of X (also known as the hyperspace of compact subsets of X), and both spaces of maps are endowed with the compact-open topology.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1412.4249

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3.0

Jun 28, 2018
06/18

by
Farshad Omidi; MohammadReza Molaei

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In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U-equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological spaces are considered.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1511.02819

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14

Jun 30, 2018
06/18

by
Piotr Kalemba; Szymon Plewik

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We present how to obtain non-comparable regular but not completely regular spaces. We analyze a generalization of Mysior's example, extracting its underlying purely set-theoretic framework. This enables us to build simple counterexamples, using the Niemytzki plane, the Songefrey plane or Lusin gaps.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1701.04322

3
3.0

Jun 30, 2018
06/18

by
Benoît Loridant; Jun Luo

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We describe non-locally connected planar continua via the concepts of fiber and numerical scale. Given a continuum $X\subset\mathbb{C}$ and $x\in\partial X$, we show that the set of points $y\in \partial X$ that cannot be separated from $x$ by any finite set $C\subset \partial X$ is a continuum. This continuum is called the {\em modified fiber} $F_x^*$ of $X$ at $x$. If $x\in X^o$, we set $F^*_x=\{x\}$. For $x\in X$, we show that $F_x^*=\{x\}$ implies that $X$ is locally connected at $x$. We...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1703.05914

3
3.0

Jun 30, 2018
06/18

by
Marita Ferrer; Salvador Hernández; Luis Tárrega

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We extend to metrizable locally compact groups Rosenthal's theorem describing those Banach spaces containing no copy of `1. For that purpose, we transfer to general locally compact groups the notion of interpolation (I0) set, which was defined by Hartman and Ryll-Nardzewsky [25] for locally compact abelian groups. Thus we prove that for every sequence fgngn

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1704.03438

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4.0

Jun 28, 2018
06/18

by
Javier Camargo; Carlos Uzcategui

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Given a continuum $X$, for each $A\subseteq X$, the Jones' set function $\mathcal{T}$ is defined by $\mathcal{T}(A)=\{x\in X : \text{for each subcontinuum }K\text{ such that }x\in \textrm{Int}(K), \text{ then }K\cap A\neq\emptyset\}.$ We show that $\mathcal{D}=\{\mathcal{T}(\{x\}):x\in X\}$ is decomposition of $X$ when $\mathcal{T}$ is continuous. We present a characterization of the continuity of $\mathcal{T}$ and answer several open questions posed by D. Bellamy.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1511.07083

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6.0

Jun 28, 2018
06/18

by
Raúl Fierro

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Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in nonlinear analysis. An application of our results is given for operators defined on locally convex spaces. The main aim of this work is to unify some well-known results existing in complete metric and vector topological spaces.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1511.07554

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6.0

Jun 28, 2018
06/18

by
K. Abodayeh; A. Pitea; W. Shatanawi; T. Abdeljawad

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In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be obtained from the corresponding results in standard metric spaces.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1512.03771

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9.0

Jun 29, 2018
06/18

by
N. H. Bingham; A. J. Ostaszewski

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The theme here is category-measure duality, in the context of a topological group. One can often handle the (Baire) category case and the (Lebesgue, or Haar) measure cases together, by working bi-topologically: switching between the original topology and a suitable refinement (a density topology). This prompts a systematic study of such density topologies, and the corresponding $\sigma$-ideals of negligibles. Such ideas go back to Weil's classic book, and to Hashimoto's ideal topologies. We...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1607.00031

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6.0

Jun 30, 2018
06/18

by
T. Banakh; S. Gabriyelyan

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Denote by $\mathbf C_p[\mathfrak M_0]$ the $C_p$-stable closure of the class $\mathfrak M_0$ of all separable metrizable spaces, i.e., $\mathbf C_p[\mathfrak M_0]$ is the smallest class of topological spaces that contains $\mathfrak M_0$ and is closed under taking subspaces, homeomorphic images, countable topological sums, countable Tychonoff products, and function spaces $C_p(X,Y)$. Using a recent deep result of Chernikov and Shelah (2014), we prove that $\mathbf C_p[\mathfrak M_0]$ coincides...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1412.2240

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7.0

Jun 29, 2018
06/18

by
Jiling Cao

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Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and other hyperspace topologies, and applications of the Wijsman topology in analysis have been explored. However, there are still several fundamental open problems on this topology. In this article, the author gives a brief survey on these problems and some...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1609.03119

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5.0

Jun 28, 2018
06/18

by
Wei He; Walter Tholen

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We extend the Dikranjan-Uspenskij notions of c-compact and h-complete topological group to the morphism level, study the stability properties of the newly defined types of maps, such as closure under direct products, and compare them with their counterparts in topology. We assume Hausdorffness only when our proofs require us to do so, which leads to new results and the affirmation of some facts that were known in a Hausdorff context.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1511.02898

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6.0

Jun 29, 2018
06/18

by
István Juhász; Jan van Mill

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Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality $\mathfrak{c}$ if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and $\sigma$-countably tight compactum has cardinality $\mathfrak{c}$ remains open. We also show that if an arbitrary product is $\sigma$-countably tight then all but finitely many of its factors must be countably tight.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1607.00517

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7.0

Jun 30, 2018
06/18

by
Jan P. Boronski; Gary Gruenhage; George Kozlowski

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We study nonmetric analogues of Vietoris solenoids. Let $\Lambda$ be an ordered continuum, and let $\vec{p}=\langle p_1,p_2,\dots\rangle$ be a sequence of positive integers. We define a natural inverse limit space $S(\Lambda,\vec{p})$, where the first factor space is the nonmetric "circle" obtained by identifying the endpoints of $\Lambda$, and the $n$th factor space, $n>1$, consists of $p_1p_2\cdot\dots \cdot p_{n-1}$ copies of $\Lambda$ laid end to end in a circle. We prove that...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1412.8508

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4.0

Jun 30, 2018
06/18

by
Robert Leek

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In this paper, we will use investigate the existence of compactifications with particular convergence properties - pseudoradial, radial, sequential and Fr\'echet-Urysohn - through the use of spoke systems.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1412.8701

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Jun 26, 2018
06/18

by
Akihiko Kitada; Shousuke Ohmori; Tomoyuki Yamamoto

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A Lambda (Card Lambda > aleph)-product space of {0,1} has a partition {X1,...,Xn} for any n a decomposition space of each Xi of which is self-similar.(February 16, 2015)

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1502.05109

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Jun 27, 2018
06/18

by
Tran Van An; Nguyen Van Dung

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In this paper, two open questions on strong $b$-metric spaces posed by Kirk and Shahzad [11, Chapter 12] are investigated. A counter-example is constructed to give a negative answer to the first question, and a theorem on the completion of a strong $b$-metric space is proved to give a positive answer to the second question.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1503.08126

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6.0

Jun 29, 2018
06/18

by
Lev Buhovsky; Eilon Solan; Omri Nisan Solan

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A set $A$ in a finite dimensional Euclidean space is \emph{monovex} if for every two points $x,y \in A$ there is a continuous path within the set that connects $x$ and $y$ and is monotone (nonincreasing or nondecreasing) in each coordinate. We prove that every open monovex set as well as every closed monovex set is contractible, and provide an example of a nonopen and nonclosed monovex set that is not contractible. Our proofs reveal additional properties of monovex sets.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1609.08844

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13

Jun 27, 2018
06/18

by
Paolo Lipparini

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The class $\mathfrak C $ relative to countably compact topological spaces and the class $\mathfrak P$ relative to pseudocompact spaces introduced by Z. Frol\'ik are naturally generalized relative to every topological property. We provide a characterization of such generalized Frol\'ik classes in the broad case of properties defined in terms of filter convergence. If a class of spaces can be defined in terms of filter convergence, then the same is true for its Frol\'ik class.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1503.02277

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Jun 27, 2018
06/18

by
Laszlo Zsilinszky

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There exists a completely metrizable bounded metrizable space $X$ with compatible metrics $d,d'$ so that the hyperspace $CL(X)$ of nonempty closed subsets of $X$ endowed with the Hausdorff metric $H_d$, $H_{d'}$, resp. is $\alpha$-favorable, $\beta$-favorable, resp. in the strong Choquet game. In particular, there exists a completely metrizable bounded metric space $(X,d)$ such that $(CL(X),H_d)$ is not completely metrizable.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1503.04383

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Jun 27, 2018
06/18

by
Taras Banakh; Alex Ravsky

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For any topological space $X$ we study the relation between the universal uniformity $\mathcal U_X$, the universal quasi-uniformity $q\mathcal U_X$ and the universal pre-uniformity $p\mathcal U_X$ on $X$. For a pre-uniformity $\mathcal U$ on a set $X$ and a word $v$ in the two-letter alphabet $\{+,-\}$ we define the verbal power $\mathcal U^v$ of $\mathcal U$ and study its boundedness numbers $\ell(\mathcal U^v)$ and $\bar \ell(\mathcal U^v)$. The boundedness numbers of the (Boolean operations...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1503.04480

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25

Jun 28, 2018
06/18

by
Richard Lupton; Max F. Pitz

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This paper investigates the space $C_k(\omega^*,\omega^*)$, the space of continuous self-maps on the Stone-\v{C}ech remainder of the integers, $\omega^*$, equipped with the compact-open topology. Our main results are that (1) $C_k(\omega^*,\omega^*)$ is Baire, (2) Stone-\v{C}ech extensions of injective maps on $\omega$ form a dense set of weak $P$-points in $C_k(\omega^*,\omega^*)$, (3) it is independent of ZFC whether $C_k(\omega^*,\omega^*)$ contains $P$-points, and that (4)...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1509.04985

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13

Jun 28, 2018
06/18

by
C. Delhomme; C. Laflamme; M. Pouzet; N. Sauer

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A metric space M is homogeneous if every isometry between finite subsets extends to a surjective isometry defined on the whole space. We show that if M is an ultrametric space, it suffices that isometries defined on singletons extend, i.e that the group of isometries of M acts transitively. We derive this fact from a result expressing that the arity of the group of isometries of an ultrametric space is at most 2. An illustration of this result with the notion of spectral homogeneity is given....

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1509.04346

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Jun 28, 2018
06/18

by
Munazza Naz; Muhammad Shabir; Muhammad Irfan Ali

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Concept of bi-soft topological spaces is introduced. Several notions of a soft topological space are generalized to study bi-soft topological spaces. Separation axioms play a vital role in study of topological spaces. These concepts have been studied in context of bi-soft topological spaces. There is a very close relationship between topology and rough set theory. An application of bi-soft topology is given in rough set theory.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1509.00866

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Jun 28, 2018
06/18

by
Isa Yildirim

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In this paper, we introduce a new type of coupled fixed point theorem in partially ordered complete metric space. We give an example to support of our result.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1507.04692

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Jun 30, 2018
06/18

by
Olena Karlova; Volodymyr Mykhaylyuk; Oleksandr Sobchuk

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We prove that for a topological space $X$, an equiconnected space $Z$ and a Baire-one mapping $g:X\to Z$ there exists a separately continuous mapping $f:X^2\to Z$ with the diagonal $g$, i.e. $g(x)=f(x,x)$ for every $x\in X$. Under a mild assumptions on $X$ and $Z$ we obtain that diagonals of separately continuous mappings $f:X^2\to Z$ are exactly Baire-one functions, and diagonals of mappings $f:X^2\to Z$ which are continuous on the first variable and Lipschitz (differentiable) on the second...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1407.5745

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3.0

Jun 29, 2018
06/18

by
Raushan Buzyakova

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We show that for any continuous monotonic fixed-point free automorphism $f$ on a $\sigma$-compact subgroup $G\subset \mathbb R$ there exists a binary operation $+_f$ such that $\langle G, +_f\rangle$ is a topological group topologically isomorphic to $\langle G, +\rangle$ and $f$ is a shift with respect to $+_f$. We then show that monotonicity cannot be replaced by the property of being periodic-point free. We explore a few routes leading to generalizations and counterexamples.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1606.05311

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6.0

Jun 28, 2018
06/18

by
Olena Karlova; Volodymyr Mykhaylyuk

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We introduce and study adhesive spaces. Using this concept we obtain a characterization of stable Baire maps $f:X\to Y$ of the class $\alpha$ for wide classes of topological spaces. In particular, we prove that for a topological space $X$ and a contractible space $Y$ a map $f:X\to Y$ belongs to the $n$'th stable Baire class if and only if there exist a sequence $(f_k)_{k=1}^\infty$ of continuous maps $f_k:X\to Y$ and a sequence $(F_k)_{k=1}^\infty$ of functionally ambiguous sets of the $n$'th...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1512.01754

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6.0

Jun 29, 2018
06/18

by
V. V. Mykhaylyuk

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It is solved the problem on constructed of separately continuous functions on product of two topological spaces with given restriction. In particular, it is shown that for every topological space $X$ and first Baire class function $g:X\to \bf R$ there exists separately continuous function $f:X\times X \to \bf R$ such that $f(x,x)=g(x)$ for every $x\in X$.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1601.07984

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3.0

Jun 29, 2018
06/18

by
Mariam Abuage; A. Kiliçman; Mohammad S. Sarsak

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Our work aims to introduce generalization of soft $ \mu $-compact soft generalized topological spaces, namely; soft nearly $ \mu $-compact spaces which are defined over initial universe with a fixed set of parameters. Basic properties and some significant corollaries will be introduced, Moreover, we investigated that a soft nearly $ \mu $-compact space produces a parametrized family of nearly $ \mu $-compact spaces. Some counter examples will be established to show that the converse may not be...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1610.01883

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14

Jun 28, 2018
06/18

by
Raushan Buzyakova; Alex Chigogidze

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We identify a class of subspaces of ordered spaces $\mathcal L$ for which the following statement holds: If $f:X\to L\in \mathcal L$ is a continuous bijections of a zero-dimensional space $X$, then $f$ can be re-routed via a zero-dimensional subspace of an ordered space that has weight not exceeding that of $L$.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1511.02849

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5.0

Jun 28, 2018
06/18

by
V. V. Mykhaylyuk

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It is studied a connection between the separability and the countable chain condition of spaces with the $L$-property (a topological space $X$ has the $L$-property if for every topological space $Y$, separately continuous function $f:X\times Y\to\mathbb R$ and open set $I\subseteq \mathbb R$ the set $f^{-1}(I)$ is a $F_{\sigma}$-set). We show that every completely regular Baire space with the $L$-property and the countable chain condition is separable and construct a nonseparable completely...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1512.07477