On the Menger and Almost Menger Properties in Locales

Authors

Tilahun Bayih, University of South Africa
Themba Dube, University of South Africa
Oghenetega Ighedo, Chapman UniversityFollow

Document Type

Article

Publication Date

4-1-2021

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 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.

Comments

This article was originally published in Applied General Topology, volume 22, issue 1, in 2021. https://doi.org/10.4995/agt.2021.14915

Recommended Citation

T. E. Bayih, T. Dube & O. Ighedo: On the Menger and almost Menger properties in locales. Appl. Gen. Topol., 22, no. 1 (2021), 199 - 221. https://doi.org/10.4995/agt.2021.14915

Peer Reviewed

1

Copyright

Applied General Topology, Universitat Politècnica de València

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.