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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Pure and Applied Algebra
( Vol. 138 NO.2 / (1999))
Weakly Pseudocompact Subsets of Nuclear Groups
W. Banaszczyk, E. Martin-Peinador,
Pages. 99-106
Abstract 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, countable 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.
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