A weak form of soft $ \alpha $-open sets and its applications via soft topologies

Tareq M. Al-shami; Abdelwaheb Mhemdi; Tareq M. Al-shami; Abdelwaheb Mhemdi

doi:10.3934/math.2023576

AIMS Mathematics

2023, Volume 8, Issue 5: 11373-11396. doi: 10.3934/math.2023576

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Research article

A weak form of soft $ \alpha $-open sets and its applications via soft topologies

Tareq M. Al-shami ^{1
,
,},
Abdelwaheb Mhemdi ²

1.
Department of Mathematics, Sana'a University, Sana'a, Yemen
2.
Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia

Received: 20 December 2022 Revised: 27 February 2023 Accepted: 05 March 2023 Published: 13 March 2023
MSC : 54A05, 03E72, 54C08

In this work, we present some concepts that are considered unique ideas for topological structures generated by soft settings. We first define the concept of weakly soft $ \alpha $-open subsets and characterize it. It is demonstrated the relationships between this class of soft subsets and some generalizations of soft open sets with the help of some illustrative examples. Some interesting results and relationships are obtained under some stipulations like extended and hyperconnected soft topologies. Then, we introduce the interior and closure operators inspired by the classes of weakly soft $ \alpha $-open and weakly soft $ \alpha $-closed subsets. We establish their master features and derive some formulas that describe the relations among them. Finally, we study soft continuity with respect to this class of soft subsets and investigate its essential properties. In general, we discuss the systematic relations and results that are missing through the frame of our study. The line adopted in this study will create new roads in the branch of soft topology.
Citation: Tareq M. Al-shami, Abdelwaheb Mhemdi. A weak form of soft $ \alpha $-open sets and its applications via soft topologies[J]. AIMS Mathematics, 2023, 8(5): 11373-11396. doi: 10.3934/math.2023576

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Abstract

In this work, we present some concepts that are considered unique ideas for topological structures generated by soft settings. We first define the concept of weakly soft $ \alpha $-open subsets and characterize it. It is demonstrated the relationships between this class of soft subsets and some generalizations of soft open sets with the help of some illustrative examples. Some interesting results and relationships are obtained under some stipulations like extended and hyperconnected soft topologies. Then, we introduce the interior and closure operators inspired by the classes of weakly soft $ \alpha $-open and weakly soft $ \alpha $-closed subsets. We establish their master features and derive some formulas that describe the relations among them. Finally, we study soft continuity with respect to this class of soft subsets and investigate its essential properties. In general, we discuss the systematic relations and results that are missing through the frame of our study. The line adopted in this study will create new roads in the branch of soft topology.

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