Abstract:We study the quasi-Menger and weakly Menger properties in locales. Our
definitions, which are adapted from topological spaces by replacing subsets
with sublocales, are conservative in the sense that a topological space is
quasi-Menger (resp. weakly Menger) if and only if the locale it determines
is quasi-Menger (resp. weakly Menger). We characterize each of these types
of locales in a language that does not involve sublocales. Regarding localic
results that have no topological counterparts, w… Show more
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