Quasi-Menger and Weakly Menger Frames

Document Type


Publication Date



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, we show that an infinitely extremally disconnected locale (in the sense of Arietta [1]) is weakly Menger if and only if its smallest dense sublocale is weakly Menger. We show that if the product of locales is quasi-Menger (or weakly Menger) then so is each factor. Even though the localic product Πj∈JΩ(Xj) is not necessarily isomorphic to the locale Ω(Πj∈JXj), we are able to deduce as a corollary of the localic result that if the product of topological spaces is weakly Menger, then so is each factor.


This article was originally published in Filomat, volume 36, issue 18, in 2022. https://doi.org/10.2298/FIL2218375B

Peer Reviewed