Methods of Generating Soft Topologies and Soft Separation Axioms

Authors

  • Zanyar A. Ameen Department of Mathematics, College of Science, University of Duhok, Iraq E-mail:
  • Ohud F. Alghamdi Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia
  • Baravan Asaad Department of Mathematics, Faculty of Science, University of Zakho, Duhok 42001, Iraq
  • Ramadhan A. Mohammed Department of Mathematics, College of Basic Education, University of Duhok, Duhok 42001, Iraq

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i2.5161

Keywords:

soft topology, soft t0, soft regular spaces

Abstract

The paper develops a novel analysis of mutual interactions between topology and soft topology. It is known that each soft topology produces a system of crisp (parameterized) topologies. The other way round is also possible. Namely, one can generate a soft topology from a system of crisp topologies. Different methods of producing soft topologies are discussed by implementing two formulas. Then, the relationships between the resulting soft topologies are obtained. With the help of an example, it is demonstrated that one formula is more constructible than the other. Now, it is reasonable to ask which (topological) properties of a soft topology can be transferred to the set of crisp topologies, or the opposite. To address this question, we consider the standard separation axioms and show how well these axioms can be preserved when moving from a system of crisp topologies to the soft topology generated by it and contrariwise. Additionally, our findings extend and disprove some results from the literature.

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Published

2024-04-30

Issue

Section

Nonlinear Analysis

How to Cite

Methods of Generating Soft Topologies and Soft Separation Axioms. (2024). European Journal of Pure and Applied Mathematics, 17(2), 1168-1182. https://doi.org/10.29020/nybg.ejpam.v17i2.5161

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