On Nearly Pseudocompact Spaces

Document Type



Mathematics (HMC)

Publication Date



A completely regular space X is called nearly pseudocompact if υXX is dense in βXX, 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(X1X2)=. It follows that a product of two nearly pseudocompact spaces, one of which is locally compact, is also nearly pseudocompact.

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© 1980 Elsevier