Results 141 to 150 of about 416 (159)

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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When does the Fell topology on a hyperspace of closed sets coincide with the meet of the upper Kuratowski and the lower Vietoris topologies?

Topology and Its Applications, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dmitri Shakhmatov, Tsugunori Nogura
exaly   +2 more sources

Reconstruction of the vietoris topology from compacta in the space of closed subgroups

Ukrainian Mathematical Journal, 1990
See the review in Zbl 0702.22009.
exaly   +2 more sources

Approximating C_free Space Topology by Constructing Vietoris-Rips Complex

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2019
We present a new way of constructing sparse roadmaps using point clouds that approximates and measures the underlying topology of the C free space. The main advantage of the constructed roadmap is its homotopy equivalence to the η-offset of the C free space.
Aakriti Upadhyay, Weifu Wang 0001, Chinwe Ekenna   +2 more
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Regular Multimeasures in the Vietoris Topology

2022
Alina Gavriluţ, Endre Pap
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Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity

2015
Summary: In this paper, we consider continuity properties (especially, regularity, also viewed as an approximation property) for \(\mathcal{P}_{0}(X)\)-valued set multifunctions (\(X\) being a linear, topological space), in order to obtain Egoroff and Lusin type theorems for set multifunctions in the Vietoris hypertopology.
Gavrilut, A., Agop, M.
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Approximation Theorems for Multimeasures in the Vietoris Topology

2022
Alina Gavriluţ, Endre Pap
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Coincidence of Vietoris and Wijsman topologies: A new proof

2009
Summary: Let \((X,d)\) be a metric space and \(\text{CL}(X)\) the family of all nonempty closed subsets of \(X\). We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric \(d\) forces \(X\) to be a compact space.
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The Contributions of L. Vietoris and H. Tietze to the Foundations of General Topology

1997
In his book on uniform structures and general topology, Andre Weil wrote in 1937 [31, footnote (1) on page 4]: “Since the composition of this work H. Cartan [7] has discovered the notion of filter which finally eliminates countability from topology by replacing the notion of sequence and permits important simplifications of the theory of uniform and ...
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A note on fibers and Vietoris topologies of paratopological groups 1

If f : G → Y is an irreducible closed continuous mapping defined on a regular weakly collectionwise normal first-countable meta-Lindelöf locally σ paratopological group G onto a T1 -space Y which has a neighborhood ωω -base at a point y ∈ Y , then f −1 (y) is σ-compact in G. We prove that if a Fréchet-Urysohn space X has strong α4-property and a weakly
Deng, Yu-Ming, Peng, Liang-Xue
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