Characterizations of sf-simple extension of topologies

Mohammed Yaseen,Raad Aziz Hussain

doi:10.52866/ijcsm.2022.02.01.003

Mohammed Yaseen, Raad Aziz Hussain

Open Access

https://doi.org/10.52866/ijcsm.2022.02.01.003

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Abstract

The main aim of this study is to create a new type of topology called “ -simple extension” and investigate its properties. We introduce a new definition for -open sets and consider this aspect as the basis of our main definition. Furthermore, we investigate the properties of the proposed concept to allow us to provide new examples of explicit descriptions of topological spaces and certain types of -covering for topological spaces, such as ( -Lindelof and -paracompact spaces). The use of the tool offers important results for topological spaces. Other findings related to the proposed approach have also been identified.

Highlights

In the domain of general topological spaces, the notion of semi-feebly was first introduced by Levine [1].A set Q of a top−s (X, ℘) is a semi-open (s-open) set if there exists an open set O of X such that O ⊆ Q ⊆cl(O), where cl(O) is the closure of O
We investigate the properties of the proposed concept to allow us to provide new examples of explicit descriptions of topological spaces and certain types of sf-covering for topological spaces, such as
We investigate a number of results concerning the sf-simple extension of topological spaces

Summary

Introduction

In the domain of general topological spaces (top−s’s), the notion of semi-feebly was first introduced by Levine [1].A set Q of a top−s (X, ℘) is a semi-open (s-open) set if there exists an open set O of X such that O ⊆ Q ⊆cl(O), where cl(O) is the closure of O. This concept has played an important role in in the research of top−s’s.

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