Vol. 99, No. 1, 1982

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Pseudocompact and Stone-Weierstrass product spaces

Robert Moffatt Stephenson Jr.

Vol. 99 (1982), No. 1, 159–174

In 1960 H. Tamano proved that for pseudocompact completely regular spaces X and Y , (i) X ×Y is pseudocompact if and only if prX 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
Received: 21 March 1980
Revised: 26 May 1980
Published: 1 March 1982
Robert Moffatt Stephenson Jr.