Uniformizing (proximal) \(\varDelta\)-topologies.
type: Item
instance of: scholarly article
title: Uniformizing (proximal) \(\varDelta\)-topologies.
zbMATH Open document ID: 1041.54026
DOI: 10.1016/S0166-8641(03)00202-5
author: E. Meccariello
author: Giuseppe Di Maio
author: S. Naimpally
published in: Topology and its Applications
publication date: 2004-03-14T00:00:00Z
review text: The authors investigate necessary and sufficient conditions for the uniformizability of (proximal) \(\Delta\)-topologies. They attack this problem using a tool from uniform topology, namely the Attouch-Wets uniformities. Similar investigations in the past have used the construction of special Urysohn functions instead. Their study also deals with uniformizability of so-called \(\Delta U\)-topologies and proximal \(\Delta U\)-topologies, which are defined as natural generalizations of the \(U\)-topology introduced by Costantini and Vitolo. Furthermore, conditions are determined under which these latter topologies are second countable, first countable or metrizable.
Mathematics Subject Classification ID: 54E05
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54B20
zbMATH DE Number: 2056846
zbMATH Keywords: proximal \(\Delta\)-topology
zbMATH Keywords: proximal \(\Delta U\)-topology
zbMATH Keywords: \(\Delta\)-topology
zbMATH Keywords: \(\Delta U\)-topology
zbMATH Keywords: Vietoris topology
zbMATH Keywords: Fell topology
zbMATH Keywords: hyperspace
zbMATH Keywords: first countability
zbMATH Keywords: second countability
zbMATH Keywords: metrizability
zbMATH Keywords: uniformity
zbMATH Keywords: proximity
zbMATH Keywords: hypertopology
zbMATH Keywords: \(\Delta\)-Attouch-Wets topology
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
cites work: Q4277838
cites work: On the Fell topology
cites work: Uniform Continuity on Bounded Sets and the Attouch-Wets Topology
cites work: Distance functionals and suprema of hyperspace topologies
cites work: Q4285972
cites work: The Infimal Value Functional and the Uniformization of Hit-and-Miss Hyperspace Topologies
cites work: On The Infimum of the Hausdorff Metric Topologies
cites work: Q4952342
cites work: Q4949727
cites work: Q3599842
cites work: Q4267489
cites work: Q3994935
cites work: A Hausdorff Topology for the Closed Subsets of a Locally Compact Non-Hausdorff Space
cites work: A topological notion of boundedness
cites work: Topologies on Spaces of Subsets
cites work: Q4098881
cites work: Q5606492
cites work: Eine Bemerkung über Trennungsaxiome in Räumen von abgeschlossenen Teilmengen topologischer Räume
cites work: Einige Bemerkungen über der Raum der abgeschlossenen Mengen
Recommended article: Q4220447
Recommended article: \(G\)-uniformities, \(LR\)-proximities and hypertopologies
Recommended article: Uniformity on generalized topological spaces
Recommended article: Uniform approximation of topological spaces
Recommended article: Functorial uniformization of topological spaces
Recommended article: Topological uniform descent and compact perturbations
Recommended article: Q4861805
Recommended article: Q5084216
Recommended article: Q4424933
Recommended article: Q4955568
description: scientific article; zbMATH DE number 2056846