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

 

On topologies of maximally almost periodic groups


Author: Ter Jenq Huang
Journal: Proc. Amer. Math. Soc. 69 (1978), 251-254
MSC: Primary 43A60; Secondary 22B05, 43A40
MathSciNet review: 0487291
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Abstract: It is proved that a necessary and sufficient condition for the group topology of any maximally almost periodic Hausdorff group to coincide with the weak topology of the group in which every complex-valued continuous almost periodic function on the group is continuous is that the group has the equivalent left and right uniform structures. The sufficiency of this condition generalizes the recent results of Glicksberg and Venkataraman concerning the group topology and the weak topology of an abelian Hausdorff group induced by the set of all continuous characters of the group.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0487291-4
PII: S 0002-9939(1978)0487291-4
Keywords: Almost periodic function, maximally almost periodic group, character of an abelian group, Pontryagin duality
Article copyright: © Copyright 1978 American Mathematical Society