On c-realcompact spaces and locally bounded normal functions

Kenneth Hardy and R. Grant Woods

Vol. 43 (1972), No. 3, 647–656

DOI: 10.2140/pjm.1972.43.647

Abstract

Let X be a completely regular Hausdorff space. Characterizations are obtained of the o-realcompact spaces lying between X and its Stone-Čech compactification βX, and of those spaces lying between X and its minimal c-realcompact extension uX. These results are used to derive several necessary and sufficient conditions for the equality E(uX) = uE(X) to hold, where E(X) is the absolute of X and uX is the Hewitt realcompactifioation of X.

Mathematical Subject Classification 2000

Primary: 54D60

Milestones

Received: 8 September 1971

Revised: 7 June 1972

Published: 1 December 1972