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?(Xj) is not necessarily isomorphic to the locale ?(?j?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.

<p>The Menger and the almost Menger properties are extended to locales. Regarding the former, the extension is conservative (meaning that a space is Menger if and only if it is Menger as a locale), and the latter is conservative for sober T_D-spaces. Non-spatial Menger (and hence almost Menger) locales do exist, so that the extensions genuinely transcend the topological notions. We also consider projectively Menger locales, and show that, as in spaces, a locale is Menger precisely when it is Lindelöf and projectively Menger. Transference of these properties along localic maps (via direct image or pullback) is considered.</p>