On the Menger and almost Menger properties in locales
Keyword(s):
<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<sub>D</sub>-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>
2021 ◽
Vol 31
(10)
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pp. 107001
Keyword(s):
2019 ◽
pp. 222-234
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Keyword(s):
2018 ◽
Vol 27
(12)
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pp. 6010-6024
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1993 ◽
Vol 5
(3)
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pp. 259-272
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