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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Vydáno v:Topological algebra and its applications Ročník 10; číslo 1; s. 246 - 254
Hlavní autor: Robdera, Mangatiana A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: De Gruyter 01.01.2022
Témata:
46A50
compactness
completeness
convex compactness
convex hull
topological vector space
total boundedness
ISSN:2299-3231, 2299-3231
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Shrnutí: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.
ISSN:2299-3231
2299-3231
DOI:10.1515/taa-2022-0131