The soft generalized closure operator and the soft topology it generates

Volume 31, Issue 1, pp 30--40 http://dx.doi.org/10.22436/jmcs.031.01.03

Publication Date: April 04, 2023 Submission Date: January 14, 2023 Revision Date: January 28, 2023 Accteptance Date: February 07, 2023

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Authors

S. Al Ghour - Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan.

Abstract

In this paper, we use soft \(g\)-closed subsets of a soft topological space \((M,\lambda ,B)\) to define a new soft closure operator and, thus, a new soft topology \(\lambda ^{\times }\) on \(M\) relative to \(B\). We show that \(\lambda ^{\times }\) contains the class of soft \(g\)-open sets, and thus \(\lambda ^{\times }\) contains \(\lambda \). We also show that \( \lambda ^{\times }\) \(=\lambda \) if and only if \((M,\lambda ,B)\) is soft \( T_{1/2}\). Furthermore, we show that \((M,\lambda ^{\times },B)\) is always soft \(T_{1/2}\), and as a result, \(\left( \lambda ^{\times }\right) ^{\times }=\lambda ^{\times }\); and we give conditions equivalent to the soft discretness of \((M,\lambda ^{\times },B)\). Furthermore, with emphasis on the transfer of "soft regularity" conditions on \((M,\lambda ,B)\) to "soft separation" conditions on \((M,\lambda ^{\times },B)\). We have also demonstrated by examples that each of soft compactness, soft connectedness, and soft second countability of \((M,\lambda ,B)\) does not transfer to \( (M,\lambda ^{\times },B)\) in general. In addition to these, we provide new properties and characterizations of the well-known concept of "soft \(g\) -continuity". Finally, we investigate the correspondences between the novel soft topological concepts and their general topological analogs.

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Keywords

• Soft \(g\)-closed sets
• soft regularity
• soft \(T_{1/2}\)
• soft \(g\)-continuity

MSC

•  54C08
•  54C10
•  54B10

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