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Completeness properties of locally quasi-convex groups

Bruguera Padró, M. Montserrat and Chasco, M.J. and Martín Peinador, Elena and Tarieladze, Vaja (2000) Completeness properties of locally quasi-convex groups. Topology and its Applications, 111 (1-2). pp. 81-93. ISSN 0166-8641

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Abstract

It is natural to extend the Grothendieck theorem on completeness, valid for locally convex topological vector spaces, to Abelian topological groups. The adequate framework to do it seems to be the class of locally quasi-convex groups. However, in this paper we present examples of metrizable locally quasi-convex groups for which the analogue to the Grothendieck theorem does not hold. By means of the continuous convergence structure on the dual of a topological group, we also state some weaker forms of the Grothendieck theorem valid for the class of locally quasi-convex groups. Finally, we prove that for the smaller class of nuclear groups, BB-reflexivity is equivalent to completeness. (C) 2001 Elsevier Science B.V.


Item Type:Article
Additional Information:

International School of Mathematics G Stampacchia 27th Course: Convergence and Topology.JUN 27-JUL 02, 1998.ERICE, ITALY

Uncontrolled Keywords:completeness; Grothendieck theorem; Pontryagin duality theorem; dual group; convergence group; continuous convergence; reflexive group; k-space; k-group; Pontryagin duality; Compact
Subjects:Sciences > Mathematics > Topology
ID Code:16660
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