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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