Soft nodec spaces

Mesfer H. Alqahtani; Zanyar A. Ameen; Mesfer H. Alqahtani; Zanyar A. Ameen

doi:10.3934/math.2024160

AIMS Mathematics

2024, Volume 9, Issue 2: 3289-3302. doi: 10.3934/math.2024160

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Research article

Soft nodec spaces

Mesfer H. Alqahtani ¹,
Zanyar A. Ameen ^{2
,
,}

1.
Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia
2.
Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq

Received: 21 November 2023 Revised: 11 December 2023 Accepted: 19 December 2023 Published: 04 January 2024
MSC : 54E99, 54F65

Following van Douwen, we call a soft topological space soft nodec if every soft nowhere dense subset of it is soft closed. This paper considers soft nodec spaces, which contain soft submaximal and soft door spaces. We investigate the basic properties and characterizations of soft nodec spaces. More precisely, we show that a soft nodec space can be written as a union of two disjoint soft closed soft dense (or soft open) soft nodec subspaces. Then, we study the behavior of soft nodec spaces under various operations, including the following: taking soft subspaces, soft products, soft topological sums, and images under specific soft functions with the support of appropriate counterexamples. Additionally, we show that the Krull dimension of a soft nodec soft $ T_{0} $-space is less than or equal to one. After that, we present some connections among soft nodec, soft strong nodec, and soft compact spaces. Finally, we successfully determine a condition under which the soft one-point compactification of a soft space is soft nodec if and only if the soft space is soft strong nodec.
- soft nodec space,
- soft submaximal space,
- soft one-point compactification,
- soft door space
Citation: Mesfer H. Alqahtani, Zanyar A. Ameen. Soft nodec spaces[J]. AIMS Mathematics, 2024, 9(2): 3289-3302. doi: 10.3934/math.2024160

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Abstract

Following van Douwen, we call a soft topological space soft nodec if every soft nowhere dense subset of it is soft closed. This paper considers soft nodec spaces, which contain soft submaximal and soft door spaces. We investigate the basic properties and characterizations of soft nodec spaces. More precisely, we show that a soft nodec space can be written as a union of two disjoint soft closed soft dense (or soft open) soft nodec subspaces. Then, we study the behavior of soft nodec spaces under various operations, including the following: taking soft subspaces, soft products, soft topological sums, and images under specific soft functions with the support of appropriate counterexamples. Additionally, we show that the Krull dimension of a soft nodec soft $ T_{0} $-space is less than or equal to one. After that, we present some connections among soft nodec, soft strong nodec, and soft compact spaces. Finally, we successfully determine a condition under which the soft one-point compactification of a soft space is soft nodec if and only if the soft space is soft strong nodec.

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