Uniformities, hyperspaces, and normality
type: Item
instance of: scholarly article
title: Uniformities, hyperspaces, and normality
zbMATH Open document ID: 0711.54004
DOI: 10.1007/BF01517358
published in: Monatshefte für Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178430
review text: Let X be a completely regular space and \(2^ X\) the hyperspace of X. It is shown that the uniform topologies induced on \(2^ X\), via the Hausdorff uniformity, from the Nachbin uniformity, which is the weak uniformity generated by C(X,R), and from the Tukey-Shirota uniformity, generated by all countable open normal coverings of X, agree. They both coincide with a Vietoris-type topology on \(2^ X\), the countable locally finite topology, iff X is normal.
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54C30
Mathematics Subject Classification ID: 54D20
zbMATH DE Number: 4169627
zbMATH Keywords: Čech uniformity
zbMATH Keywords: uniform topology
zbMATH Keywords: proximal hypertopology
zbMATH Keywords: hyperspace
zbMATH Keywords: Hausdorff uniformity
zbMATH Keywords: Nachbin uniformity
zbMATH Keywords: Tukey-Shirota uniformity
zbMATH Keywords: countable locally finite topology
author: Anna Di Concilio
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4169627