Vol. 110, No. 2, 1984

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ISSN: 0030-8730
On the G-compactification of products

Jan de Vries

Vol. 110 (1984), No. 2, 447–470
Abstract

Let βGX denote the maximal equivariant compactification (G-compactification) of the G-space X (i.e. a topological space X, completely regular and Hausdorff, on which the topological group G acts as a continuous transformation group). If G is locally compact and locally connected, then we show that βG(X × Y ) = βGX × βGY if and only if X × Y is what we call G-pseudocompact, provided X and Y satisfy a certain non-triviality condition. This result generalizes Glicksberg’s well-known result about Stone-Čech compactifications of products to the case of topological transformation groups.

Mathematical Subject Classification 2000
Primary: 54D35
Secondary: 54D30, 54H15
Milestones
Received: 14 December 1981
Published: 1 February 1984
Authors
Jan de Vries