Supra soft Omega-open sets and supra soft Omega-regularity

Dina Abuzaid; Samer Al-Ghour; Dina Abuzaid; Samer Al-Ghour

doi:10.3934/math.2025303

AIMS Mathematics

2025, Volume 10, Issue 3: 6636-6651. doi: 10.3934/math.2025303

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Research article

Supra soft Omega-open sets and supra soft Omega-regularity

Dina Abuzaid ¹,
Samer Al-Ghour ^{2
,
,}

1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
Correction on: AIMS Mathematics 10: 10624-10625.

Received: 05 February 2025 Revised: 12 March 2025 Accepted: 19 March 2025 Published: 25 March 2025
MSC : 05C72, 54A40

This paper introduces a novel concept of supra-soft topology generated from a specific family of supra-topologies. We define supra-soft $ \omega $-open sets as a new class of soft sets that create a finer topology than the original. We explore the properties of these supra-soft $ \omega $-open sets and assess the validity of related results from ordinary supra-topological spaces within the framework of supra-soft topological spaces. Additionally, we present two new separation axioms: supra-soft $ \omega $-local indiscreteness and supra-soft $ \omega $ -regularity, demonstrating that both are stronger than traditional supra-soft $ \omega $-regularity. We also provide subspace and product theorems for supra-soft $ \omega $-regularity and examine the correspondence between our new supra-soft concepts and their classical counterparts in supra-topology.
- supra-$ \omega $-open sets,
- supra-$ \omega $-local indiscrete space,
- supra-soft regular space,
- supra-generated soft topology
Citation: Dina Abuzaid, Samer Al-Ghour. Supra soft Omega-open sets and supra soft Omega-regularity[J]. AIMS Mathematics, 2025, 10(3): 6636-6651. doi: 10.3934/math.2025303

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Abstract

This paper introduces a novel concept of supra-soft topology generated from a specific family of supra-topologies. We define supra-soft $ \omega $-open sets as a new class of soft sets that create a finer topology than the original. We explore the properties of these supra-soft $ \omega $-open sets and assess the validity of related results from ordinary supra-topological spaces within the framework of supra-soft topological spaces. Additionally, we present two new separation axioms: supra-soft $ \omega $-local indiscreteness and supra-soft $ \omega $ -regularity, demonstrating that both are stronger than traditional supra-soft $ \omega $-regularity. We also provide subspace and product theorems for supra-soft $ \omega $-regularity and examine the correspondence between our new supra-soft concepts and their classical counterparts in supra-topology.

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