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