Pontryagin duality for topological Abelian groups |
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Authors: | Salvador Hernández |
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Institution: | (1) Universidad Jaume I, Departamento de Matemáticas, Campus de Riu Sec, 12071 Castellón, Spain (hernande@mat.uji.es), ES |
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Abstract: | A topological Abelian group G is Pontryagin reflexive, or P-reflexive for short, if the natural homomorphism of G to its bidual group is a topological isomorphism. We look at the question, set by Kaplan in 1948, of characterizing the topological
Abelian groups that are P-reflexive. Thus, we find some conditions on an arbitrary group G that are equivalent to the P-reflexivity of G and give an example that corrects a wrong statement appearing in previously existent characterizations of P-reflexive groups.
Received: 10 February 2000 / Published online: 17 May 2001 |
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Keywords: | Mathematics Subject Classification (1991): 22A05 43A40 54H11 46A20 |
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