On Nearly Pseudocompact Spaces

Authors

Melvin Henriksen, Harvey Mudd CollegeFollow
Marlon C. Rayburn, University of Manitoba

Document Type

Article

Department

Mathematics (HMC)

Publication Date

5-1980

Abstract

A 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(X₁X₂)=. It follows that a product of two nearly pseudocompact spaces, one of which is locally compact, is also nearly pseudocompact.

Rights Information

© 1980 Elsevier

DOI

10.1016/0166-8641(80)90005-X

Recommended Citation

Henriksen, Melvin and Rayburn, Marlon C. 1980. On nearly pseudocompact spaces. Topology and its Applications. 11(2):161-172.