On theG-compactification of products
Jan de Vries · Pacific Journal of Mathematics · 1984
Let β G X denote the maximal equivariant compactiίication (G-compactίfication) 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 β G (XX Y) = β G X X β G Y if and only if X 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-Cech compactifications of products to the case of topological transformation groups.