Work

Reversibility of Tk-topological spaces and the universality problem for the collection of Tk-topological spaces

Year: 2025

Type: article

Abstract: As a generalization of the Khalimsky line topological space, consider the topological space (Z, Tk) (resp. (Z, T?k)) on the set of integers, where the topology Tk (resp. T?k) is generated by the set Sk (resp. S?k) as a subbase, k ? Z, and Sk:= {Sk,t | Sk,t:= {2t, 2t + 1, 2t + 2k + 1}, t ? Z} (resp. S?k:= {S?k,t | S?k,t:= {2t,2t+1,2t + 2k } ,t? Z }).For k ? Z \ {0}, each of the Tk- and T? k-topological space indeed satisfies the T1/2-separation axiom. Besides, for k ? Z \ {0}, each of (Z, Tk) and (Z, T?k) is an Alexandroff space and is neither a Kuratowski space nor a regular space. The paper initially proves that each of (Z, Tk) and (Z, T?k), k ? Z, is reversible. Next, let T be the collection of Tk-topological spaces {(Z, Tk), k ? Z \ {0}}, and T? be the set of T?k-topological spaces {(Z, T?k), k ? Z \ {0}}. Then the paper deals with an existence problem of a universal element in T and T?.

Source: Filomat

DOI: 10.2298/fil2505585l

Authors: Sik Lee, Sang-Eon Han

Institutions: Chonnam National University, Jeonbuk National 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 Research Foundation of Korea, Ministry of Education, Science and Technology

Awards: G5066884915, G5439953842