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An extension theorem for functions on semigroups

Author: Paul Milnes
Journal: Proc. Amer. Math. Soc. 55 (1976), 152-154
MSC: Primary 43A60
MathSciNet review: 0420153
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Abstract: For $ S$ a semitopological semigroup, a continuous function on $ S$ is said to be in $ LMC(S)$ if its set of right translates is relatively compact in $ C(S)$ for the topology of pointwise convergence on $ S$. It is proved here that, if $ S$ is a dense subsemigroup of a topological group $ G$, then every function in $ LMC(S)$ extends to a function continuous on $ G$. This result generalizes earlier results that were arrived at independently by A. T. Lau and the present author. Some corollaries of this result are also presented.

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Keywords: Topological semigroup, continuous function, almost periodic function, uniform continuity, extension
Article copyright: © Copyright 1976 American Mathematical Society

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