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Pontryagin reflexive groups are not determined by their continuous characters

Martín Peinador, Elena and Chasco, M.J. (1998) Pontryagin reflexive groups are not determined by their continuous characters. Rocky Mountain Journal of Mathematics, 28 (1). pp. 155-160. ISSN 0035-7596

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A theorem of Glicksberg states that, for an abelian group G, two locally compact topologies with the same set of continuous characters must coincide. In [12] it is asserted that this fact also holds for two Pontryagin reflexive topologies. We prove here that this statement is not correct, and we give some additional conditions under which it is true. We provide some examples of classes of groups determined by their continuous characters.

Item Type:Article
Uncontrolled Keywords:Continuous character; reflexive space; compact-open topology; Pontryagin duality; Glicksberg theorem; Montel space
Subjects:Sciences > Mathematics > Topology
ID Code:16699

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Last Modified:07 Feb 2014 09:34

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