Soft separation axioms via soft topological operators

Tareq M. Al-shami; Zanyar A. Ameen; A. A. Azzam; Mohammed E. El-Shafei; Tareq M. Al-shami; Zanyar A. Ameen; A. A. Azzam; Mohammed E. El-Shafei

doi:10.3934/math.2022828

AIMS Mathematics

2022, Volume 7, Issue 8: 15107-15119. doi: 10.3934/math.2022828

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Research article

Soft separation axioms via soft topological operators

1.
Department of Mathematics, Sana'a University, Sana'a, Yemen
2.
Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq
3.
Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt
5.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

Received: 07 April 2022 Revised: 24 May 2022 Accepted: 13 June 2022 Published: 15 June 2022
MSC : 54C60, 54A05, 54A99

This paper begins with an introduction to some soft topological operators that will be used to characterize several soft separation axioms followed by their main properties. Then, we define a new soft separation axiom called "soft $ T_D $-space" and analyze its main properties. We also show that this space precisely lies between soft $ T_0 $ and soft $ T_1 $-spaces. Finally, we characterize soft $ T_i $-spaces, for $ i = 0, 1, D $, in terms of the stated operators.
- soft topology,
- soft operator,
- soft shell,
- soft kernel,
- soft derived set,
- soft $ T_0 $-space,
- soft $ T_1 $-space,
- soft $ T_D $-space
Citation: Tareq M. Al-shami, Zanyar A. Ameen, A. A. Azzam, Mohammed E. El-Shafei. Soft separation axioms via soft topological operators[J]. AIMS Mathematics, 2022, 7(8): 15107-15119. doi: 10.3934/math.2022828

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Abstract

This paper begins with an introduction to some soft topological operators that will be used to characterize several soft separation axioms followed by their main properties. Then, we define a new soft separation axiom called "soft $ T_D $-space" and analyze its main properties. We also show that this space precisely lies between soft $ T_0 $ and soft $ T_1 $-spaces. Finally, we characterize soft $ T_i $-spaces, for $ i = 0, 1, D $, in terms of the stated operators.

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