Martín Peinador, Elena and Bruguera Padró, M. Montserrat (1996) Open subgroups, compact subgroups amd BinzButzmannn reflexivity. Topology and its Applications, 72 (2). pp. 101111. ISSN 01668641

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Abstract
A number of attempts to extend Pontryagin duality theory to categories of groups larger than that of locally compact abelian groups have been made using different approaches. The extension to the category of topological abelian groups created the concept of reflexive group. In this paper we deal with the extension of Pontryagin duality to the category of convergence abelian groups. Reflexivity in this category was defined and studied by E. Binz and H. Butzmann. A convergence group is reflexive (subsequently called BBreflexive by us in our work) if the canonical embedding into the bidual is a convergence isomorphism.
Topological abelian groups are, in an obvious way, convergence groups; therefore it is natural to compare reflexivity and BBreflexivity for them. Chasco and MartínPeinador (1994) show that these two notions are independent. However some properties of reflexive groups also hold for BBreflexive groups, and the purpose of this paper is to show two of them. Namely, we prove that if an abelian topological group G contains an open subgroup A, then G is BBreflexive if and only if A is BBreflexive. Next, if G has sufficiently many continuous characters and K is a compact subgroup of G, then G is BBreflexive if and only if G/K is BBreflexive.
Item Type:  Article 

Uncontrolled Keywords:  Reflexive group; Continuous convergence structure; Character; Dual group 
Subjects:  Sciences > Mathematics > Topology 
ID Code:  12705 
Deposited On:  11 May 2011 09:40 
Last Modified:  06 Feb 2014 09:30 
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