Compactness Principles for Topological Vector Spaces

We show that the many of the canonical quantifications of interrelated concepts, centered around compactness in the setting of metric spaces, can be easily generalized to the setting of topological linear spaces. Among other things, we obtain a generalization of the Hausdorff Total Boundedness Princ...

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Published in:Topological algebra and its applications Vol. 10; no. 1; pp. 246 - 254
Main Author: Robdera, Mangatiana A.
Format: Journal Article
Language:English
Published: De Gruyter 01.01.2022
Subjects:
46A50
compactness
completeness
convex compactness
convex hull
topological vector space
total boundedness
ISSN:2299-3231, 2299-3231
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Abstract We show that the many of the canonical quantifications of interrelated concepts, centered around compactness in the setting of metric spaces, can be easily generalized to the setting of topological linear spaces. Among other things, we obtain a generalization of the Hausdorff Total Boundedness Principle, of the Grothendieck Compactness Principle, as well as of the Convex Compactness Principle for topological vector spaces.
AbstractList We show that the many of the canonical quantifications of interrelated concepts, centered around compactness in the setting of metric spaces, can be easily generalized to the setting of topological linear spaces. Among other things, we obtain a generalization of the Hausdorff Total Boundedness Principle, of the Grothendieck Compactness Principle, as well as of the Convex Compactness Principle for topological vector spaces.
Author Robdera, Mangatiana A.
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  givenname: Mangatiana A.
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  organization: Department of Mathematics, University of Botswana, 4775 Notwane Road, Gaborone, Botswana
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Cites_doi 10.1090/S0002-9939-2010-10508-7
10.1080/00029890.1952.11988056
10.1016/j.jfa.2012.05.014
10.1090/memo/0016
10.1016/j.jmaa.2013.08.050
10.4064/sm150-1-3
10.1007/s11579-010-0024-z
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Snippet We show that the many of the canonical quantifications of interrelated concepts, centered around compactness in the setting of metric spaces, can be easily...
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StartPage 246
SubjectTerms 46A50
compactness
completeness
convex compactness
convex hull
topological vector space
total boundedness
Title Compactness Principles for Topological Vector Spaces
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