A note on weakly pseudocompact locales

Themba Dube

Abstract

We revisit weak pseudocompactness in pointfree topology, and show that a locale is weakly pseudocompact if and only if it is Gδ-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 Gδ-sublocales are spatial inherit weak pseudocompactness from the factors. We also show that if a locale is weakly pseudocompact and its Gδ-sublocales are complemented then it is Baire.


Keywords

Frame; locale; sublocale; Gδ-sublocale; weakly pseudocompact; binary coproduct

Subject classification

Primary: 06D22; Secondary: 54E17.

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