THE EQUIVALENCE OF COMPACTNESS AND PSEUDO-COMPACTNESS IN SOME FUNCTION SPACES

This paper investigates the relationship between compactness and pseudo-compactness in subsets of C(X) where X is locally compact and first countable. Two primary theorems are proven. First, equicontinuity at a point is proven to be equivalent to the existence of a certain open cover of a pseudo-compact subset of C(X). The second theorem proves the equivalence of compactness and pseudo-compctness for closed subsets F of C(X).