Pseudo-completeness of the compact-open topology on C(X)

Abstract

This paper gives an answer to a question raised by R.A. McCoy about the pseudo-completeness of Ck(X). In this paper it has been shown that if Ck(X) is pseudo-complete, then every closed hemicompact subset of X is a k-space and is C-embedded in X. It is also shown that the converse of this also holds for the class of topological spaces that are either perfect image of a topological sum of hemicompact spaces or that can be mapped onto a topological sum of hemicompact spaces by a perfect map.