Work

The semi-T3-separation axiom of Khalimsky topological spaces

Year: 2023

Type: article

Abstract: The paper initially studies both the s-T3-separation and the semi-T3-separation axiom of Khalimsky (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 homeomorphism, 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.

Source: Filomat

DOI: 10.2298/fil2308539h

Authors: Sang-Eon Han, Selma Özçağ

Institutions: Jeonbuk National University, Hacettepe University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Research Foundation, National Natural Science Foundation of China, National Research Foundation of Korea, Ministry of Education, Science and Technology

Awards: G5066884915, G5439953842