A note on weakly pseudocompact locales

Abstract

We revisit weak pseudocompactness in pointfree topology, and show that a locale is weakly pseudocompact if and only if it is G δ -dense in some compactification. This localic approach (in contrast with the earlier frame-theoretic one) enables us to show that finite localic products of locales whose non-void G δ -sublocales are spatial inherit weak pseudocompactness from the factors. We also show that if a locale is weakly pseudocompact and its G δ -sublocales are complemented then it is Baire.