ABSTRACT. It is proved here that a completely regular Hausdorff space X is pseudocompact if and only if for any continuous function f from X to a pseudo-, compact space (or a compact space) Y, f # is z-ultrafilter whenever is a z-ultrafilter on X.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.