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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Official URL: http://www.sciencedirect.com/science/article/pii/S0022404998000346

## 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, 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 |
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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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Deposited On: | 11 Oct 2012 09:02 |

Last Modified: | 07 Feb 2014 09:34 |

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