Topological extensions of product spaces

Frank Kost

Vol. 108 (1983), No. 1, 129–132

DOI: 10.2140/pjm.1983.108.129

Abstract

The Stone-Čech compactification βX and the Hewitt real-compactification vX [6] of a completely regular T₁-space X can be obtained as certain spaces of ultrafilters from the collection of zero sets of members of C^∗(X) [4]. With the appropriate structure βX is the space of all ultrafilters and vX those with the countable intersection property. In this framework we give a necessary and sufficient condition for βX × βY ≈ β(X × Y ).

Mathematical Subject Classification 2000

Primary: 54D35

Secondary: 54B10, 54C50

Milestones

Received: 8 February 1982

Published: 1 September 1983