Novel categories of supra soft continuous maps via new soft operators

Alaa M. Abd El-latif; Mesfer H. Alqahtani; Alaa M. Abd El-latif; Mesfer H. Alqahtani

doi:10.3934/math.2024361

AIMS Mathematics

2024, Volume 9, Issue 3: 7449-7470. doi: 10.3934/math.2024361

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Novel categories of supra soft continuous maps via new soft operators

Alaa M. Abd El-latif ^1,2,
Mesfer H. Alqahtani ^{3
,
,}

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
3.
Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia

Received: 07 January 2024 Revised: 04 February 2024 Accepted: 08 February 2024 Published: 21 February 2024
MSC : 54A05, 54B10, 03E72, 54C10

In this paper we continue presenting new types of soft operators for supra soft topological spaces (or SSTSs). Specifically, we investigate more interesting properties and relationships between the supra soft somewhere dense interior (or SS-sd-interior) operator, the SS-sd-closure operator, the SS-sd-cluster operator, and the SS-sd-boundary operator. We prove that the SS-sd-interior operator, SS-sd-boundary operator, and SS-sd-exterior operator form a partition for the absolute soft set. Furthermore, we apply the notion of SS-sd-sets to soft continuity. In addition, we use the SS-sd-interior operator and the SS-sd-closure operator to provide equivalent conditions and many characterizations for SS-sd-continuous, SS-sd-irresolute, SS-sd-open, SS-sd-closed, and SS-sd-homeomorphism maps. Examples include the following: The soft mapping is an SS-sd-homeomorphism if, and only if it is both SS-sd-continuous and an SS-sd-closed if, and only if, the soft mapping in addition to its inverse is SS-sd-continuous. Moreover, a bijective soft mapping is SS-sd-open if, and only if, it is SS-sd-closed. Furthermore, we provide many examples and counterexamples to show our results, which are extensions of previous studies. A diagram summarizing our results is also introduced.
- supra soft sd-operators,
- supra soft sd-interior points,
- supra soft sd-continuous maps,
- supra soft sd-homeomorphism maps,
- applications
Citation: Alaa M. Abd El-latif, Mesfer H. Alqahtani. Novel categories of supra soft continuous maps via new soft operators[J]. AIMS Mathematics, 2024, 9(3): 7449-7470. doi: 10.3934/math.2024361

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Abstract

In this paper we continue presenting new types of soft operators for supra soft topological spaces (or SSTSs). Specifically, we investigate more interesting properties and relationships between the supra soft somewhere dense interior (or SS-sd-interior) operator, the SS-sd-closure operator, the SS-sd-cluster operator, and the SS-sd-boundary operator. We prove that the SS-sd-interior operator, SS-sd-boundary operator, and SS-sd-exterior operator form a partition for the absolute soft set. Furthermore, we apply the notion of SS-sd-sets to soft continuity. In addition, we use the SS-sd-interior operator and the SS-sd-closure operator to provide equivalent conditions and many characterizations for SS-sd-continuous, SS-sd-irresolute, SS-sd-open, SS-sd-closed, and SS-sd-homeomorphism maps. Examples include the following: The soft mapping is an SS-sd-homeomorphism if, and only if it is both SS-sd-continuous and an SS-sd-closed if, and only if, the soft mapping in addition to its inverse is SS-sd-continuous. Moreover, a bijective soft mapping is SS-sd-open if, and only if, it is SS-sd-closed. Furthermore, we provide many examples and counterexamples to show our results, which are extensions of previous studies. A diagram summarizing our results is also introduced.

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