Results 11 to 20 of about 416 (159)

An adaptation of the Vietoris topology for ordered compact sets

Applied General Topology
We introduce a natural topology on powers of a space that is inspired by the Vietoris topology on compact subsets. We then place this topology in context with other product topologies; specifically, we compare this topology with the Tychonoff product ...
Christopher Caruvana, Jared Holshouser
doaj   +4 more sources

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, Jan Pelant, László Zsilinszky   +2 more
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CL(R) is simply connected under the Vietoris topology

Applied General Topology, 2007
In this paper we present a proof by construction that the hyperspace CL(R) of closed, nonemtpy subsets of R is simply connected under the Vietoris topology. This is useful in considering the convergence of time scales.
N.C. Esty
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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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Calix[4]arene Design for Enhanced Carbon Capture via Topological Learning. [PDF]

Chemistry
ABSTRACT Solid direct air capture (S‐DAC) technologies have the potential to remove pre‐existing CO2 from the atmosphere by taking advantage of hydrophobic materials that will retain CO2 through physisorption and separating it from the abundant water molecules. Calix[n]arenes are highly tunable and versatile complexes with inherent hydrophobic cavities,
Laub JA, Vogiatzis KD.
europepmc   +2 more sources

On the Infimum of the Hausdorff and Vietoris Topologies [PDF]

Proceedings of the American Mathematical Society, 1993
We study the infimum of the Hausdorff and Vietoris topologies on the hyperspace of a metric space. We show that this topology coincides with the supremum of the upper Hausdorff and lower Vietoris topologies if and only if the underlying metric space is either totally bounded or is a UC space.
S. Levi, LUCCHETTI, ROBERTO, J. Pelant
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A Note on Hyperspaces by Closed Sets with Vietoris Topology

Bulletin of the Malaysian Mathematical Sciences Society, 2022
17pages
Liu, Chuan, Lin, Fucai
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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
Bouziad, Ahmed, Hola, L'Ubica, Zsilinszky, László   +2 more
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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 ...
Cao, J, Tomita, AH
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The hyperspaces Cn(X) for finite ray-graphs

Applied General Topology, 2013
In this paper we consider the hyperspace Cn(X) of non-empty and closed subsets of a base space X with up to n connected components. The class of base spaces we consider we call finite ray-graphs, and are a noncompact variation on finite graphs.
Norah Esty
doaj   +1 more source