Three new soft separation axioms in soft topological spaces
Soft $ \omega $-almost-regularity, soft $ \omega $ -semi-regularity, and soft $ \omega $-$ T_{2\frac{1}{2}} $ as three novel soft separation axioms are introduced. It is demonstrated that soft $ \omega $ -almost-regularity is strictly between "soft regularity" and "soft almost-regular...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024223?viewType=HTML |
| _version_ | 1797323860321763328 |
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| author | Dina Abuzaid Samer Al Ghour |
| author_facet | Dina Abuzaid Samer Al Ghour |
| author_sort | Dina Abuzaid |
| collection | DOAJ |
| description | Soft $ \omega $-almost-regularity, soft $ \omega $ -semi-regularity, and soft $ \omega $-$ T_{2\frac{1}{2}} $ as three novel soft separation axioms are introduced. It is demonstrated that soft $ \omega $ -almost-regularity is strictly between "soft regularity" and "soft almost-regularity"; soft $ \omega $-$ T_{2\frac{1}{2}} $ is strictly between "soft $ T_{2\frac{1}{2}} $" and "soft $ T_{2} $", and soft $ \omega $ -semi-regularity is a weaker form of both "soft semi-regularity" and "soft $ \omega $-regularity". Several sufficient conditions for the equivalence between these new three notions and some of their relevant ones are given. Many characterizations of soft $ \omega $-almost-regularity are obtained, and a decomposition theorem of soft regularity by means of "soft $ \omega $ -semi-regularity" and "soft $ \omega $-almost-regularity" is obtained. Furthermore, it is shown that soft $ \omega $-almost-regularity is heritable for specific kinds of soft subspaces. It is also proved that the soft product of two soft $ \omega $-almost regular soft topological spaces is soft $ \omega $-almost regular. In addition, the connections between our three new conceptions and their topological counterpart topological spaces are discussed. |
| first_indexed | 2024-03-08T05:34:12Z |
| format | Article |
| id | doaj.art-adf2d7e2d0914f4fb3886baf91c78da2 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:34:12Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-adf2d7e2d0914f4fb3886baf91c78da22024-02-06T01:32:42ZengAIMS PressAIMS Mathematics2473-69882024-01-01924632464810.3934/math.2024223Three new soft separation axioms in soft topological spacesDina Abuzaid 0Samer Al Ghour11. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia2. Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, JordanSoft $ \omega $-almost-regularity, soft $ \omega $ -semi-regularity, and soft $ \omega $-$ T_{2\frac{1}{2}} $ as three novel soft separation axioms are introduced. It is demonstrated that soft $ \omega $ -almost-regularity is strictly between "soft regularity" and "soft almost-regularity"; soft $ \omega $-$ T_{2\frac{1}{2}} $ is strictly between "soft $ T_{2\frac{1}{2}} $" and "soft $ T_{2} $", and soft $ \omega $ -semi-regularity is a weaker form of both "soft semi-regularity" and "soft $ \omega $-regularity". Several sufficient conditions for the equivalence between these new three notions and some of their relevant ones are given. Many characterizations of soft $ \omega $-almost-regularity are obtained, and a decomposition theorem of soft regularity by means of "soft $ \omega $ -semi-regularity" and "soft $ \omega $-almost-regularity" is obtained. Furthermore, it is shown that soft $ \omega $-almost-regularity is heritable for specific kinds of soft subspaces. It is also proved that the soft product of two soft $ \omega $-almost regular soft topological spaces is soft $ \omega $-almost regular. In addition, the connections between our three new conceptions and their topological counterpart topological spaces are discussed.https://www.aimspress.com/article/doi/10.3934/math.2024223?viewType=HTMLsoft almost regularitysoft $ \omega $ -opennesssoft $ r\omega $-opennesssoft regularitysoft $ \omega $ -regularitysoft semi-regularity |
| spellingShingle | Dina Abuzaid Samer Al Ghour Three new soft separation axioms in soft topological spaces AIMS Mathematics soft almost regularity soft $ \omega $ -openness soft $ r\omega $-openness soft regularity soft $ \omega $ -regularity soft semi-regularity |
| title | Three new soft separation axioms in soft topological spaces |
| title_full | Three new soft separation axioms in soft topological spaces |
| title_fullStr | Three new soft separation axioms in soft topological spaces |
| title_full_unstemmed | Three new soft separation axioms in soft topological spaces |
| title_short | Three new soft separation axioms in soft topological spaces |
| title_sort | three new soft separation axioms in soft topological spaces |
| topic | soft almost regularity soft $ \omega $ -openness soft $ r\omega $-openness soft regularity soft $ \omega $ -regularity soft semi-regularity |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024223?viewType=HTML |
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