β-Normality in locales

• Ngcamphalala, Thobile ^[1] ; Nxumalo, Mbekezeli ^[1]
  1. [1] Rhodes University

     Rhodes University

     Makana, Sudáfrica

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 1, 2025, págs. 543-574
• Idioma: inglés
• DOI: 10.4995/agt.2025.22790
• Enlaces
  • Texto completo
• Resumen

  • 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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