Pseudocompact and Stone-Weierstrass product spaces

Robert Moffatt Stephenson Jr.

Vol. 99 (1982), No. 1, 159–174

DOI: 10.2140/pjm.1982.99.159

Abstract

In 1960 H. Tamano proved that for pseudocompact completely regular spaces X and Y , (i) X ×Y is pseudocompact if and only if pr_X is z-closed, and (ii) X ×Y is pseudocompact if one of X and Y is a k-space.

In 1979 C. E. Aull asked if every product of functionally regular SW spaces is an SW space, and he proved that for a family of functionally regular SW spaces, (iii) their product is an SW space if and only if it is pseudocompact.

The main results of this paper will answer Aull’s question affirmatively and prove that (i), (ii), and (iii) hold for strongly functionally Hausdorff spaces.

Mathematical Subject Classification 2000

Primary: 54B10

Secondary: 54D99

Milestones

Received: 21 March 1980

Revised: 26 May 1980

Published: 1 March 1982