β-Normality in locales
Year: 2025
Type: article
Abstract: In this paper, we establish the theory of β-normal locales which are the point- free counterparts of β-normal spaces which were introduced by Arkhangel’skii and Ludwig. We give characterizations of β-normal locales using some types of open sublocales. Certain circumstances are exhibited in which normality coincides with β-normality. For instance, we use the localic Kateˇtov-Tong insertion theorem to prove that every β-normal locale which is also a coframe is normal. This result argues that there does not exist a finite β-normal locale which is not normal. Included here is also an answer to Murtinova ́’s question about the existence of a regular β-normal space which is not Tychonoff. The study of β-normal locales leads to some variants of β-normal locales, namely α-normal locales and almost weakly β-normal locales. This paper also examines preservation and reflection of β-normal locales by localic maps.
Source: Applied General Topology
Authors: Thobile Ngcamphalala, Mbekezeli Nxumalo
Institution: Rhodes University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: National Research Foundation
Award: G4476552800
OpenAlex ID: W4409049048