Open AccessSoft separation axioms and functions with soft closed graphs
Author(s) -
Alias B. Khalaf,
Nehmat K. Ahmed,
Qumri H. Hamko
Publication year - 2022
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-4004
Subject(s) - topological space , soft set , separation axiom , closed set , mathematics , closure (psychology) , axiom , topology (electrical circuits) , discrete mathematics , pure mathematics , computer science , combinatorics , geometry , artificial intelligence , economics , market economy , fuzzy logic
Several notions on soft topology are studied and their basic properties are investigated by using the concept of soft open sets and soft closure operators which are derived from the basics of soft set theory established by Molodtsov [7]. In this paper we introduce some soft separation axioms called Soft R0 and soft R1 in soft topological spaces which are defined over an initial universe with a fixed set of parameters. Many characterizations and properties of these spaces are found. Necessary and sufficient conditions for a soft topological space to be a soft Ri for i = 0, 1 space are also presented. Furthermore, the concept of functions with soft closed graph and soft cluster sets are defined. Many results on theses two concepts are proved also it is proved that a function has a soft closed graph if and only if its soft cluster set is degenerate.