Soft structural Oxtoby–Rose operators and their generated topologies

Zanyar A. Ameen; Ohud F. Alghamdi; Zanyar A. Ameen; Ohud F. Alghamdi

doi:10.3934/math.2025930

AIMS Mathematics

2025, Volume 10, Issue 9: 20825-20842. doi: 10.3934/math.2025930

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Soft structural Oxtoby–Rose operators and their generated topologies

Zanyar A. Ameen ^{1
,
,},
Ohud F. Alghamdi ²

1.
Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq
2.
Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia

Received: 12 June 2025 Revised: 02 September 2025 Accepted: 05 September 2025 Published: 10 September 2025
MSC : 54A10, 54A99, 03E99

In this study, we introduce the notion of soft Oxtoby–Rose operators within the framework of abstract measurable soft spaces, extend the classical concept of lower-density operators, and explore their essential characteristics. Subsequently, we delve into the so-called soft Oxtoby–Rose topologies (soft OR-topologies), the soft topologies generated by soft Oxtoby–Rose operators. We examine the key features and definitions associated with soft OR-topologies. Specifically, we demonstrate that within soft OR-topologies, Baire category soft sets, soft locally closed sets, and Borel soft sets are all equivalent. We wrap up this research by analyzing various soft topological properties linked to soft OR-topologies.
- soft Oxtoby–Rose operator,
- lower-density soft operator,
- soft topology,
- soft density topology
Citation: Zanyar A. Ameen, Ohud F. Alghamdi. Soft structural Oxtoby–Rose operators and their generated topologies[J]. AIMS Mathematics, 2025, 10(9): 20825-20842. doi: 10.3934/math.2025930

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Abstract

In this study, we introduce the notion of soft Oxtoby–Rose operators within the framework of abstract measurable soft spaces, extend the classical concept of lower-density operators, and explore their essential characteristics. Subsequently, we delve into the so-called soft Oxtoby–Rose topologies (soft OR-topologies), the soft topologies generated by soft Oxtoby–Rose operators. We examine the key features and definitions associated with soft OR-topologies. Specifically, we demonstrate that within soft OR-topologies, Baire category soft sets, soft locally closed sets, and Borel soft sets are all equivalent. We wrap up this research by analyzing various soft topological properties linked to soft OR-topologies.

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