Soft nodec spaces
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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://aimspress.com/article/doi/10.3934/math.2024160?viewType=HTML |
| _version_ | 1797348730880393216 |
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| author | Mesfer H. Alqahtani Zanyar A. Ameen |
| author_facet | Mesfer H. Alqahtani Zanyar A. Ameen |
| author_sort | Mesfer H. Alqahtani |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T12:10:11Z |
| format | Article |
| id | doaj.art-f74e92c8dccd47f7b5f79060726d9098 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T12:10:11Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-f74e92c8dccd47f7b5f79060726d90982024-01-23T01:30:55ZengAIMS PressAIMS Mathematics2473-69882024-01-01923289330210.3934/math.2024160Soft nodec spacesMesfer H. Alqahtani0Zanyar A. Ameen 11. Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia2. Department of Mathematics, College of Science, University of Duhok, Duhok 42001, IraqFollowing 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.https://aimspress.com/article/doi/10.3934/math.2024160?viewType=HTMLsoft nodec spacesoft submaximal spacesoft one-point compactificationsoft door space |
| spellingShingle | Mesfer H. Alqahtani Zanyar A. Ameen Soft nodec spaces AIMS Mathematics soft nodec space soft submaximal space soft one-point compactification soft door space |
| title | Soft nodec spaces |
| title_full | Soft nodec spaces |
| title_fullStr | Soft nodec spaces |
| title_full_unstemmed | Soft nodec spaces |
| title_short | Soft nodec spaces |
| title_sort | soft nodec spaces |
| topic | soft nodec space soft submaximal space soft one-point compactification soft door space |
| url | https://aimspress.com/article/doi/10.3934/math.2024160?viewType=HTML |
| work_keys_str_mv | AT mesferhalqahtani softnodecspaces AT zanyaraameen softnodecspaces |