On nearly pseudocompact spaces

AbstractA completely regular space X is called nearly pseudocompact if υX−X is dense in βX−X, where βX is the Stone-Čech compactification of X and υX is its Hewitt realcompactification. After characterizing nearly pseudocompact spaces in a variety of ways, we show that X is nearly pseudocompact if it has a dense locally compact pseudocompact subspace, or if no point of X has a closed realcompact neighborhood. Moreover, every nearly pseudocompact space X is the union of two regular closed subsets X1, X2 such that Int X1 is locally compact, no points of X2 has a closed realcompact neighborhood, and Int(X1⌢X2)=∅. It follows that a product of two nearly pseudocompact spaces, one of which is locally compact, is also nearly pseudocompact