INCLUSION RELATIONS CONCERNING WEAKLY ALMOST PERIODIC FUNCTIONS AND FUNCTIONS VANISHING AT INFINITY (Journal of Sciences, Islamic Republic of Iran)
We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? 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