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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reflexivity of topological groups


Author: Peter Nickolas
Journal: Proc. Amer. Math. Soc. 65 (1977), 137-141
MSC: Primary 22A05
MathSciNet review: 0486276
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Abstract: It is shown that under mild conditions the path-component of the identity in the dual group $ G\hat \emptyset $ of an Abelian topological group G is precisely the union of the one-parameter subgroups of $ G\hat \emptyset $. This yields several corollaries, including a necessary condition for certain groups to be reflexive (to satisfy the Pontrjagin duality theorem), and a negative answer to a question of N. Noble.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0486276-0
PII: S 0002-9939(1977)0486276-0
Keywords: Dual group, Pontrjagin duality theorem, reflexive, free Abelian topological group, $ {k_\omega }$-space
Article copyright: © Copyright 1977 American Mathematical Society