Results 11 to 20 of about 521,410 (206)
Journal of Scientific Research, 2016 In this article, we define the hyperspace of soft closed sets of a soft topological space (F A , τ). In addition, we define the Vietoris soft topology, τ v , by determining the soft base of this topology which has the form ⟨F H1 , F H2 ,.....F Hn ...
Q. R. Shakir
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Developable hyperspaces are metrizable
Applied General Topology, 2003 Developability of hyperspace topologies (locally finite, (bounded) Vietoris, Fell, respectively) on the nonempty closed sets is characterized. Submetrizability and having a Gδ-diagonal in the hyperspace setting is also discussed.
L'Ubica Holá +2 more
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Coincidence of the upper Vietoris topology and the Scott topology [PDF]
Topology and its Applications, 2020 For a $T_0$ space $X$, let $\mk (X)$ be the poset of all compact saturated sets of $X$ with the reverse inclusion order. The space $X$ is said to have property Q if for any $K_1, K_2\in \mk (X)$, $K_2\ll K_1$ in $\mk (X)$ if{}f $K_2\subseteq \ii~\!K_1$.
Xiaoquan Xu, Zhongqiang Yang
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Some Connectedness and Related Property of Hyperspace with Vietoris Topology
Proceedings of the 2015 International Conference on Modeling, Simulation and Applied Mathematics, 2015 For a Hausdorff space X , we denote by 2 the collection of all closed subsets of X . In this paper, we discuss the connectedness and locally connectedness of hyperspace 2 endowed with the vietoris topology. Further path connectedness is investigated. The
Meili Zhang, B. Deng, Yu'e Yang, P. Che
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An Approach to the Concept of Soft Vieotoris Topology
International Journal of Analysis and Applications, 2016 In the present paper, we study the Vietoris topology in the context of soft set. Firstly, we investigate some aspects of first countability in the soft Vietoris topology. Then, we obtain some properties about its second countability.
Izzettin Demir
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On hereditary Baireness of the Vietoris topology
Topology and its Applications, 2001 It is shown that a metrizable space X, with completely metrizable separable closed subspaces, has a hereditarily Baire hyperspace K(X) of nonempty compact subsets of X endowed with the Vietoris topology tv. In particular, making use of a construction of Saint Raymond, we show in ZFC that there exists a non-completely metrizable, metrizable space X with
A. Bouziad, L. Holá, L. Zsilinszky
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Continuity of p-variation in the Vietoris topology
Journal of Mathematical Analysis and Applications, 2008 Let \(f:[0,1]\rightarrow \mathbb{R}\) be a real-valued function and \(p>0\). For any nonempty closed subset \(A\) of \([0,1]\), we call \(A\)-family any collection \(\mathcal{T}=\{I_{i}\}\) of non-overlapping subintervals of \([0,1]\) with end-points in \(A\) and we define the \(p\)-variation \(v_{p}(f,A)\) of \(f\) on \(A\) to be the supremum of the ...
F. Prus-Wiśniowski
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Baire spaces, Tychonoff powers and the Vietoris topology [PDF]
Proceedings of the American Mathematical Society, 2007 In this paper, we show that if the Tychonoff power X ω X^\omega of a quasi-regular space X X is Baire, then its Vietoris hyperspace 2 X 2^X is also Baire. We also provide two examples to show (i) the converse of this result does not hold in general, and (ii) the ...
Jiling Cao, A. H. Tomita
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Vietoris topology on partial maps with compact domains
Topology and its Applications, 2010 Let \(K(X)\) denote the space of all compact subsets of a Hausdorff space \(X\) with the Vietoris topology \(\tau_V\). For Hausdorff spaces \(X\) and \(Y\) and for \(B \subseteq X\), let \(C(B, Y)\) denote the set of all continuous maps from \(B\) to \(Y\) and \({ \mathcal P} _K(X,Y)\) the set of all partial maps with compact domains, that is ...
L. Holá, L. Zsilinszky
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Relations approximated by continuous functions in the Vietoris topology
Fundamenta Mathematicae, 2007 LetX be a Tikhonov space,C(X) be the space of all continuous real- valued functions defined onX, and CL(X × R) be the hyperspace of all nonempty closed subsets ofX × R. We prove the following result: LetX be a locally connected locally compact paracompact space, and letF 2 CL(X × R).
L. Holá, R. A. Mccoy
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