Between the Classes of Soft Open Sets and Soft Omega Open Sets

Samer Al Ghour

doi:10.3390/math10050719

Abstract

In this paper, we define the class of soft ω0-open sets. We show that this class forms a soft topology that is strictly between the classes of soft open sets and soft ω-open sets, and we provide some sufficient conditions for the equality of the three classes. In addition, we show that soft closed soft ω-open sets are soft ω0-open sets in soft Lindelof soft topological spaces. Moreover, we study the correspondence between soft ω0-open sets in soft topological spaces and ω0-open sets in topological spaces. Furthermore, we investigate the relationships between the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of a given soft anti-locally countable soft topological space and the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of the soft topological space of soft ω0-open sets generated by it. Finally, we introduce ω0-regularity in topological spaces via ω0-open sets, which is strictly between regularity and ω-regularity, and we also introduce soft ω0-regularity in soft topological spaces via soft ω0-open sets, which is strictly between soft regularity and soft ω-regularity. We investigate relationships regarding ω0-regularity and soft ω0-regularity. Moreover, we study the correspondence between soft ω0-regularity in soft topological spaces and ω0-regularity in topological spaces.

Highlights

Some problems in medicine, engineering, the environment, economics, sociology, and other fields have their own doubts
With the help of examples, we show that this class of soft sets forms a soft topology that lies strictly between the soft topology of soft open sets and the soft topology of soft ω0-open sets, and we give some sufficient conditions for the equality between the three soft topologies
We show that soft closed soft ω-open sets are soft ω0-open sets in soft Lindelof soft topological spaces

Summary

Introduction

Some problems in medicine, engineering, the environment, economics, sociology, and other fields have their own doubts. As one of the main branches of mathematics, is the branch of topology that deals with the basic definitions of set theory and structures used in topology. It is the foundation of most other branches of topology, including algebraic topology, geometric topology, and differential topology. We extend ω0-open sets to include soft topological spaces. We investigate this class of soft sets, especially in soft Lindelof and soft anti-locally soft topological spaces.

Preliminaries

Soft ω0-Regularity

Conclusions