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Weakly pseudocompact subsets of nuclear groups

Martín Peinador, Elena and Banaszczyk, W (1999) Weakly pseudocompact subsets of nuclear groups. Journal of Pure and Applied Algebra , 138 (2). pp. 99-106. ISSN 0022-4049

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Let G be an Abelian topological group and G(+) the group G endowed with the weak topology induced by continuous characters. We say that G respects compactness (pseudocompactness, countable compactness, functional boundedness) if G and G+ have the same compact (pseudocompact, countably compact, functionally bounded) sets. The well-known theorem of Glicksberg that LCA groups respect compactness was extended by Trigos-Arrieta to pseudocompactness and functional boundedness. In this paper we generalize these results to arbitrary nuclear groups, a class of Abelian topological groups which contains LCA groups and nuclear locally convex spaces and is closed with respect to subgroups, separated quotients and arbitrary products.

Item Type:Article
Uncontrolled Keywords:locally compact Abelian group; nuclear groups; nuclear locally convex spaces; compactness; countable compactness; pseudocompactness; functional boundedness; Abelian groups
Subjects:Sciences > Mathematics > Topology
ID Code:16691

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