Nonseparability of quotient spaces of function algebras on topological semigroups

Author:
Heneri A. M. Dzinotyiweyi

Journal:
Trans. Amer. Math. Soc. **272** (1982), 223-235

MSC:
Primary 43A60; Secondary 22A20

MathSciNet review:
656487

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a topological semigroup, the space of all bounded real-valued continuous functions on . We define the subspace of consisting of all weakly uniformly continuous functions and the space of all weakly almost periodic functions in .

Among other results, for a large class of topological semigroups , for which noncompact locally compact topological groups are a very special case, we prove that the quotient spaces and, for nondiscrete , are nonseparable. (The actual setting of these results is more general.) For locally compact topological groups, parts of our results answer affirmatively certain questions raised earlier by Ching Chou and E. E. Granirer.

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DOI:
https://doi.org/10.1090/S0002-9947-1982-0656487-6

Keywords:
Topological semigroup,
uniformly continuous functions,
weakly almost periodic functions

Article copyright:
© Copyright 1982
American Mathematical Society