Results 131 to 140 of about 416 (159)

The Vietoris topology on rectifiable spaces

Semigroup Forum, 2013
In this paper the hyperspace \(C(G)\) of compact subsets of a rectifiable space \(G\) endowed with the Vietoris topology is studied. It is shown that this topological space is a right loop if and only if the cardinality of \(G\) is 1 and that, for a locally compact rectifiable space \(G\), the semi-right loop \(C(G)\) is a topological semi-right loop.
Fucai Lin, Lin Fucai
exaly   +3 more sources

Selections for Vietoris-Like Hyperspace Topologies

Proceedings of the London Mathematical Society, 2000
The authors prove a selection theorem for a Vietoris-like hyperspace topology related to a special clopen base \({\mathcal B}\) of a space \(X\): Theorem 2.1 Let \(X\) be a completely metrizable space which has a clopen \({\mathcal D}\)-orderable base for some \({\mathcal D}\subseteq{\mathcal F}(x)\) (\({\mathcal F}(x)\) denoting the non-empty closed ...
Gutev, Valentin, Nogura, Tsugunori
exaly   +2 more sources

Topology becomes algebraic with Vietoris and Noether

Journal of Pure and Applied Algebra, 1986
The author points out that homology groups were formally introduced simultaneously by Emmy Noether and Leopold Vietoris in 1926 and produces evidence that the Göttingen and Vienna schools were independent in this achievement. He also quotes a letter from Vietoris in which the latter writes ''Without doubt H.
Saunders Mac Lane
exaly   +3 more sources

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 ...
László Zsilinszky, L'Ubica Holá
exaly   +2 more sources

Generalized metric properties on hyperspaces with the Vietoris topology

Rocky Mountain Journal of Mathematics, 2021
The paper investigates the hyperspace of the compact subsets, as well as of the finite subsets of a \(T_3\)-space \(X\) endowed with the Vietoris topology having subbase elements that hit open subsets of \(X\), and miss closed subsets of \(X\), respectively.
Lin, Fucai, Shen, Rongxin, Liu, Chuan
openaire   +2 more sources

Continuity properties and Alexandroff theorem in Vietoris topology

Fuzzy Sets and Systems, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +2 more sources

The relationship between the Vietoris topology and the Hausdorff quasi-uniformity

Topology and Its Applications, 2002
One early result in the study of hyperspace quasi-uniformities is that the Hausdorff quasi-uniformity of a Pervin quasi-uniformity of a topological space \(X\) induces the Vietoris topology on the family of nonempty subsets of \(X\), see [\textit{N. Levine} and \textit{W. J. Stager jun.}, Math. J. Okayama Univ. 15, 101-106 (1972; Zbl 0246.54033)].
Jesus Rodríguez-López, Salvador Romaguera   +1 more
exaly   +2 more sources

Nonstandard development of the vietoris topology

Lecture Notes in Mathematics, 1991
exaly   +2 more sources

The upper Vietoris topology on the space of inverse-closed subsets of a spectral space and applications [PDF]

Rocky Mountain Journal of Mathematics, 2018
Given an arbitrary spectral space $X$, we consider the set ${\boldsymbol{\mathcal{X}}}(X)$ of all nonempty subsets of $X$ that are closed with respect to the inverse topology. We introduce a Zariski-like topology on ${\boldsymbol{\mathcal{X}}}(X)$ and, after observing that it coincides the upper Vietoris topology, we prove that ${\boldsymbol{\mathcal{X}
Carmelo Antonio Finocchiaro, Dario Spirito, Marco FONTANA   +2 more
exaly   +5 more sources

The Vietoris Topology

1996
exaly   +2 more sources