Complete metrizability of topologies of strong uniform convergence on bornologies
type: Item
instance of: scholarly article
title: Complete metrizability of topologies of strong uniform convergence on bornologies
zbMATH Open document ID: 1234.54025
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-01-04T00:00:00Z
review text: It is well-known that if \(X\) is locally compact and Lindelöf then the compact-open topology on the set of real-valued continuous functions is completely metrizable, see \textit{R. F. Arens} [Ann. Math. (2) 47, 480--495 (1946; Zbl 0060.39704)]; the key property here is that there is a countable family of compact sets whose interiors cover~\(X\). The author generalizes this to topological spaces with a bornology (an ideal of nonempty subsets that also covers the space). Under suitable assumptions including that the bornology has a countable cofinal family consisting of closed sets, one can characterize (complete) metrizability of the topology of strong uniform convergence on members of the bornology.
reviewed by: K. P. Hart
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 46A17
Mathematics Subject Classification ID: 54E50
zbMATH DE Number: 5994338
zbMATH Keywords: bornology
zbMATH Keywords: complete metrizability
zbMATH Keywords: strong uniform convergence
zbMATH Keywords: shield
author: Ľubica Holá
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.09.031
OpenAlex ID: W1997679392
cites work: Between compactness and completeness
cites work: Bornological convergence and shields
cites work: The bornology of cofinally complete subsets
cites work: Strong uniform continuity
cites work: Total boundedness and bornologies
cites work: Uniform continuity, uniform convergence, and shields
cites work: Boundedness, one-point extensions and B-extensions
cites work: Arzelà's theorem and strong uniform convergence on bornologies
cites work: Q4132979
cites work: Boundedness in a topological space
cites work: Q3226265
cites work: Bornological convergences
cites work: Completeness properties of function spaces
DOI: 10.1016/J.JMAA.2011.09.031
description: scientific article; zbMATH DE number 5994338