Geodesic
Quasi-Menger and weakly Menger frames
Filomat, Tome 36 (2022) no. 18, p. 6375

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DOI

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 j∈J Ω(X j) is not necessarily isomorphic to the locale Ω j∈J X j , 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.
DOI : 10.2298/FIL2218375B
Classification : 06D22, 54A35, 54B05, 54C10, 54D20
Keywords: Frame, locale, Menger, quasi-Menger, weakly Menger, sublocale 
Tilahun Bayih; Themba Dube; Oghenetega Ighedo. Quasi-Menger and weakly Menger frames. Filomat, Tome 36 (2022) no. 18, p. 6375 . doi: 10.2298/FIL2218375B
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     author = {Tilahun Bayih and Themba Dube and Oghenetega Ighedo},
     title = {Quasi-Menger and weakly {Menger} frames},
     journal = {Filomat},
     pages = {6375 },
     year = {2022},
     volume = {36},
     number = {18},
     doi = {10.2298/FIL2218375B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2218375B/}
}
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