On the Menger and almost Menger properties in locales

On the Menger and almost Menger properties in locales

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...

Full description

Bibliographic Details
Main Authors: Tilahun Bayih, Themba Dube, Oghenetega Ighedo
Format: Article
Language:English
Published: Universitat Politècnica de València 2021-04-01
Series:Applied General Topology
Subjects:
menger
almost menger
frame
locale
sublocale
spectrum of a frame
Online Access:https://polipapers.upv.es/index.php/AGT/article/view/14915
Description
Summary: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.
ISSN:1576-9402
1989-4147

Similar Items