On topologies of maximally almost periodic groups

Huang, Ter Jenq

doi:10.1090/S0002-9939-1978-0487291-4

On topologies of maximally almost periodic groups
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Proc. Amer. Math. Soc. 69 (1978), 251-254 Request permission

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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