Novel types of supra soft operators via supra soft sd-sets and applications

Alaa M. Abd El-latif; Alaa M. Abd El-latif

doi:10.3934/math.2024321

AIMS Mathematics

2024, Volume 9, Issue 3: 6586-6602. doi: 10.3934/math.2024321

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Novel types of supra soft operators via supra soft sd-sets and applications

Alaa M. Abd El-latif ^{1,2
,
,}

1.
Mathematics Department, College of Sciences and Arts, Northern Border University, Rafha 91911, Saudi Arabia
2.
Mathematics Department, Faculty of Education, Ain Shams University, Roxy, 11341, Cairo, Egypt

Received: 21 December 2023 Revised: 12 January 2024 Accepted: 25 January 2024 Published: 06 February 2024
MSC : 54A05, 54B05, 54C10

Our purpose in this work is to present a new generalized soft open set in supra soft topological spaces, named supra soft sd-sets. With deep discussion, we found out that they contain almost all kinds of weaker supra soft open sets which have been discussed in earlier studies, as shown in the following figure.

So, directly we can notice the value of the introduced results. Also, the notion of a supra soft sc-set is presented, and many of its basic properties are explored. Furthermore, we show that the new family fails to form soft topology or supra soft topology. In addition, the definitions of the supra soft sd-closure operator, supra soft sd-cluster operator, and supra soft sd- interior operator are introduced, and many of their interesting properties are explored. Finally, we prove that the property of being a supra soft sd-set is a supra soft topological property.
- supra soft somewhere dense sets,
- supra soft operators,
- supra soft sc-sets,
- supra soft neighbourhood,
- applications
Citation: Alaa M. Abd El-latif. Novel types of supra soft operators via supra soft sd-sets and applications[J]. AIMS Mathematics, 2024, 9(3): 6586-6602. doi: 10.3934/math.2024321

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Abstract

Our purpose in this work is to present a new generalized soft open set in supra soft topological spaces, named supra soft sd-sets. With deep discussion, we found out that they contain almost all kinds of weaker supra soft open sets which have been discussed in earlier studies, as shown in the following figure.

So, directly we can notice the value of the introduced results. Also, the notion of a supra soft sc-set is presented, and many of its basic properties are explored. Furthermore, we show that the new family fails to form soft topology or supra soft topology. In addition, the definitions of the supra soft sd-closure operator, supra soft sd-cluster operator, and supra soft sd- interior operator are introduced, and many of their interesting properties are explored. Finally, we prove that the property of being a supra soft sd-set is a supra soft topological property.

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