Selectively pseudocompact groups and p-compactness

Abstract

We say that a space X is selectively pseudocompact if for each sequence (Un)n<ω of nonempty open subsets of X there is a sequence (xn)n<ω of points in X such that xn∈Un, for each n<ω, and the set {xn:n<ω} has a cluster point in X. We prove that if p and q are not equivalent selective ultrafilters on ω, then there are a p-compact group and a q-compact group whose product is not selectively pseudocompact.