On the Menger and almost Menger properties in locales

Tilahun Bayih, Themba Dube, Oghenetega Ighedo

Abstract

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 TD-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.


Keywords

Menger; almost Menger; frame; locale; sublocale; spectrum of a frame

Subject classification

06D22; 54C05; 54D20.

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References

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Universitat Politècnica de València

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