Results 161 to 170 of about 521,410 (206)

Generalized metric properties on hyperspaces with the Vietoris topology

Rocky Mountain Journal of Mathematics, 2019
We study the heredity of the classes of generalized metric spaces (for example, spaces with a $\sigma$-hereditarily closure-preserving $k$-network, spaces with a point-countable base, spaces with a base of countable order, spaces with a point-regular ...
Fucai Lin, R. Shen, Chuan Liu
semanticscholar   +3 more sources

Approximating Cfree 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 Cfree space. The main advantage of the constructed roadmap is its homotopy equivalence to the η-offset of the Cfree ...
Aakriti Upadhyay, Weifu Wang, Chinwe Ekenna   +2 more
semanticscholar   +2 more sources

The Vietoris topology on rectifiable spaces

Semigroup Forum, 2014
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
semanticscholar   +4 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
semanticscholar   +2 more sources

A note on fibers and Vietoris topologies of paratopological groups

Quaestiones Mathematicae
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 ...
Yuanyuan Deng, Liang-Xue Peng
semanticscholar   +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.
Alina Gavriluţ
semanticscholar   +2 more sources

Nonstandard development of the vietoris topology

, 1991
K. Wicks
semanticscholar   +2 more sources

Approximation theorems for fuzzy set multifunctions in Vietoris topology: Physical implications of regularity

Atomicity through Fractal Measure Theory, 2019
Alina Gavriluţ, I. Mercheş, M. Agop
semanticscholar   +2 more sources

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.
Alina Gavriluţ, M. Agop
semanticscholar   +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
openaire   +1 more source