Some Results Related to Soft Topological Spaces

TL;DR

This paper explores properties of soft topological spaces, including soft compactness and separation axioms, revealing that classical topological results do not always hold in the soft setting.

Contribution

It introduces results on soft compactness and separation axioms, and demonstrates that some classical theorems fail in soft topological spaces.

Findings

Soft compactness and countably soft compactness are studied.

Some classical topological results do not hold in soft topological spaces.

A specific soft topological space is constructed to illustrate these differences.

Abstract

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft separation axioms that have been studied by Min and Shabir-Naz. By constructing a special soft topological space, show that some classical results in general topology are not true about soft topological spaces, for instance every compact Housdorff spaces need not be normal.