The semi-T3-separation axiom of Khalimsky topological spaces

Han S., ÖZÇAĞ S.

Filomat, vol.37, no.8, pp.2539-2559, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 8
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2308539h
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.2539-2559
  • Keywords: Semi-open, semi-closed, semi-T3-space, s-T3-space, Alexandroff space, semi-regular, semi-T1-space, semi-T2-space, Khalimsky topology, semi-homeomorphism, s-regular
  • Hacettepe University Affiliated: Yes

Abstract

The paper initially studies both the s-T3-separation and the semi-T3-separation axiom of Khalim-sky (K-for brevity) topological spaces. To do this work, first we investigate some properties of semi-open and semi-closed sets with respect to the operations of union or intersection and further, a homeomor-phism, and a semi-homeomorphism. Next, we study various properties of semi-topological properties of K-topological spaces such as simple K-paths. Finally, after introducing the notion of a semi-T3-separation axiom which is broader than the s-T3-separation axiom, we find a sufficient and necessary condition for a Khalimsky topological space to satisfy the semi-T3-separation axiom.