Results 1 to 10 of about 707 (188)

Vietoris topology on spaces dominated by second countable ones

Open Mathematics, 2015
For a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = {FK : K ∈ C(M)} ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂
Islas Carlos, Jardon Daniel
doaj   +5 more sources

CL(R) is simply connected under the Vietoris topology [PDF]

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
doaj   +6 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   +3 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 A Finocchiaro, Marco FONTANA, Dario Spirito   +2 more
exaly   +7 more sources

Coincidence of the upper Vietoris topology and the Scott topology [PDF]

Topology and Its Applications, 2021
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
exaly   +3 more sources

Persistent homology for MCI classification: a comparative analysis between graph and Vietoris-Rips filtrations [PDF]

Frontiers in Neuroscience
IntroductionMild cognitive impairment (MCI), often linked to early neurodegeneration, is associated with subtle disruptions in brain connectivity. In this paper, the applicability of persistent homology, a cutting-edge topological data analysis technique
Debanjali Bhattacharya, Debanjali Bhattacharya, Rajneet Kaur, Ninad Aithal, Ninad Aithal, Neelam Sinha, Thomas Gregor Issac   +6 more
doaj   +2 more sources

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 ...
Franciszek Prus-Wiśniowski
exaly   +2 more sources

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
doaj   +3 more sources

Selection principles of the Fell topology and the Vietoris topology

Topology and Its Applications, 2016
For a noncompact Hausdorff space \(X\), let \(\text{CL} (X)\) be the family of all nonempty closed subsets of \(X\). Let \(\tau _F\) (resp., \(\tau_V\)) denote the Fell (resp., Vietoris) topology on \(\text{CL} (X)\). Motivated by \textit{G. Di Maio} et al. [Topology Appl. 153, No. 5--6, 912--923 (2005; Zbl 1087.54007)], the author investigates several
Zuquan Li
exaly   +2 more sources