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.
