β-Normality in locales
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 nor...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2025-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/22790 |
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| Summary: | 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. |
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| ISSN: | 1576-9402 1989-4147 |