Wallman compactifications on E-completely regular spaces

Norma Mary Piacun and Li Pi Su

Vol. 45 (1973), No. 1, 321–326

DOI: 10.2140/pjm.1973.45.321

Abstract

The Wallman space on E-completely regular spaces is considered. Let ℱ be the family of all E-closed subsets of an E-completely regular space X. Then the Wallman space 𝒲(X,ℱ) is a compactification of X. In particular, if E is such that I = [0,1] is E-completely regular, then 𝒲(X,ℱ) is an E-compactification. An example is given to show that I being E-completely regular is necessary.

Mathematical Subject Classification 2000

Primary: 54D35

Milestones

Received: 3 November 1971

Revised: 1 May 1972

Published: 1 March 1973