INCLUSION RELATIONS CONCERNING WEAKLY ALMOST PERIODIC FUNCTIONS AND FUNCTIONS VANISHING AT INFINITY

摘要

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X, π) and show that if X is a locally compact noncompact uniform space, and π is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show that the conditions we have imposed on the transformation semigroup are almost essential for the inclusion to hold.