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A survey on strong reflexivity of abelian topological groups

Martín Peinador, Elena and Chasco, M.J. A survey on strong reflexivity of abelian topological groups. Topology and its Applications . ISSN 0166-8641 (Submitted)

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Abstract

An Abelian topological group is called strongly reflexive if every closed subgroup and every Hausdorff quotient of the group and of its dual group are reflexive. In the class of locally compact Abelian groups (LCA) there is no need to define "strong reflexivity": it does not add anything new to reflexivity, which by the Pontryagin - van Kampen Theorem
is known to hold for every member of the class. In this survey we collect how much of "reflexivity" holds for diferent classes of groups, with especial emphasis in the classes of pseudocompact groups, !-groups and P-groups, in which some reexive groups have been
recently detected. In section 3.5 we complete the duality relationship between the classes of P-groups and !-bounded groups, already outlined in [26].
By no means we can claim completeness of the survey: just an ordered view of the topic, with some small new results indicated in the text

Item Type:Article
Uncontrolled Keywords:Pontryagin duality theorem, Dual group, Reflexive group, Strongly reflexive group, Metrizable group, Čech-complete group, ω-bounded group, P-group
Subjects:Sciences > Mathematics > Topology
ID Code:12713
Deposited On:13 May 2011 11:08
Last Modified:06 Feb 2014 09:31

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