On soft pc-separation axioms

Qumri H Hamko,Alias B Khalaf,Nehmat K Ahmed

doi:10.1515/dema-2020-0003

Qumri H Hamko, Alias B Khalaf + Show 1 more

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https://doi.org/10.1515/dema-2020-0003

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Abstract

AbstractMany mathematicians defined and studied soft separation axioms and soft continuity in soft spaces by using ordinary points of a topological space X. Also, some of them studied the same concepts by using soft points. In this paper, we introduce the concepts of soft {p}_{c}-{T}_{i} and soft {p}_{c}-{T}_{i}^{\ast }, i=0,1,2 by using the concept of soft {p}_{c}-open sets in soft topological spaces. We explore several properties of such spaces. We also investigate the relationship among these spaces and provide a counter example when it is needed.

Highlights

After the introduction of soft set theory for the first time by Molodtsov [1] in 1999 as a new tool in mathematics to deal with several kinds of vagueness in complicated problems in sciences, the study of soft sets and their properties was applied to many branches of mathematics such as probability theory, algebra, operation research, and mathematical analysis
In the last two decades, mathematicians turned their studies towards soft topological spaces and they reported in several papers different and many interesting topological concepts
It is noticed that a soft topological space gives a parametrized family of topologies on the initial universe but the converse is not true, i.e., if some topologies are given for each parameter, we cannot construct a soft topological space from the given topologies

Summary

Introduction

After the introduction of soft set theory for the first time by Molodtsov [1] in 1999 as a new tool in mathematics to deal with several kinds of vagueness in complicated problems in sciences, the study of soft sets and their properties was applied to many branches of mathematics such as probability theory, algebra, operation research, and mathematical analysis. Shabir and Naz [4] in 2011 introduced the concept of soft topological spaces which are defined over an initial universe with fixed set of parameters. Hamko and Ahmed [13] introduced the concepts of soft pc-open (soft pc closed) sets, soft pc-neighbourhood and soft pc-closure They defined and discussed the properties of soft pc-interior, soft pc-exterior and soft pc-boundary. The aim of this paper is to introduce and discuss a study of soft separation axioms, soft Pc − Ti, soft Pc − Ti⁎ (i = 0, 1, 2), soft pc-regular and soft pc-normal spaces, which are defined over an initial universe with a fixed set of parameters by using soft points defined in [11]. Any logical operation (λ) on soft sets in soft topological spaces is denoted by usual set of theoretical operations with symbol (s (λ))

Preliminaries

Conclusion