A note on weakly pseudocompact locales
Submitted: 2016-09-27
|Accepted: 2017-01-06
|Published: 2017-04-03
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Keywords:
Frame, locale, sublocale, Gδ-sublocale, weakly pseudocompact, binary coproduct
Supporting agencies:
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.
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