On Soft Generalized <i>ω</i>-Closed Sets and Soft <i>T</i><sub>1/2</sub> Spaces in Soft Topological Spaces
In this paper, we define a soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed set, which is a generalization of both th...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-04-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/11/5/194 |
| _version_ | 1797501576284209152 |
|---|---|
| author | Samer Al Ghour |
| author_facet | Samer Al Ghour |
| author_sort | Samer Al Ghour |
| collection | DOAJ |
| description | In this paper, we define a soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed set, which is a generalization of both the soft <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed set and the soft generalized closed set. We show that the classes of generalized closed sets and generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed sets coincide in soft anti-locally countable soft topological spaces. Additionally, in soft locally countable soft topological spaces, we show that every soft set is a soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed set. Furthermore, we prove that the classes of soft generalized closed sets and soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed sets coincide in the soft topological space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>X</mi><mo>,</mo><msub><mi>τ</mi><mi>ω</mi></msub><mo>,</mo><mi>A</mi><mo>)</mo></mrow></semantics></math></inline-formula>. In addition to these, we determine the behavior of soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed sets relative to soft unions, soft intersections, soft subspaces, and generated soft topologies. Furthermore, we investigate soft images and soft inverse images of soft generalized closed sets and soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed sets under soft continuous, soft closed soft transformations. Finally, we continue the study of soft <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></semantics></math></inline-formula> spaces, in which we obtain two characterizations of these soft spaces, and investigate their behavior with respect to soft subspaces, soft transformations, and generated soft topologies. |
| first_indexed | 2024-03-10T03:20:26Z |
| format | Article |
| id | doaj.art-687ee9883c2c4592841d835067f6bd29 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T03:20:26Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-687ee9883c2c4592841d835067f6bd292023-11-23T10:03:54ZengMDPI AGAxioms2075-16802022-04-0111519410.3390/axioms11050194On Soft Generalized <i>ω</i>-Closed Sets and Soft <i>T</i><sub>1/2</sub> Spaces in Soft Topological SpacesSamer Al Ghour0Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, JordanIn this paper, we define a soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed set, which is a generalization of both the soft <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed set and the soft generalized closed set. We show that the classes of generalized closed sets and generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed sets coincide in soft anti-locally countable soft topological spaces. Additionally, in soft locally countable soft topological spaces, we show that every soft set is a soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed set. Furthermore, we prove that the classes of soft generalized closed sets and soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed sets coincide in the soft topological space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>X</mi><mo>,</mo><msub><mi>τ</mi><mi>ω</mi></msub><mo>,</mo><mi>A</mi><mo>)</mo></mrow></semantics></math></inline-formula>. In addition to these, we determine the behavior of soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed sets relative to soft unions, soft intersections, soft subspaces, and generated soft topologies. Furthermore, we investigate soft images and soft inverse images of soft generalized closed sets and soft generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-closed sets under soft continuous, soft closed soft transformations. Finally, we continue the study of soft <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></semantics></math></inline-formula> spaces, in which we obtain two characterizations of these soft spaces, and investigate their behavior with respect to soft subspaces, soft transformations, and generated soft topologies.https://www.mdpi.com/2075-1680/11/5/194soft ω-open setgeneralized closed sets<i>T</i><sub>1/2</sub> spacesgeneralized ω-closed setssoft <i>T</i><sub>1/2</sub> spacessoft generated soft topological spaces |
| spellingShingle | Samer Al Ghour On Soft Generalized <i>ω</i>-Closed Sets and Soft <i>T</i><sub>1/2</sub> Spaces in Soft Topological Spaces Axioms soft ω-open set generalized closed sets <i>T</i><sub>1/2</sub> spaces generalized ω-closed sets soft <i>T</i><sub>1/2</sub> spaces soft generated soft topological spaces |
| title | On Soft Generalized <i>ω</i>-Closed Sets and Soft <i>T</i><sub>1/2</sub> Spaces in Soft Topological Spaces |
| title_full | On Soft Generalized <i>ω</i>-Closed Sets and Soft <i>T</i><sub>1/2</sub> Spaces in Soft Topological Spaces |
| title_fullStr | On Soft Generalized <i>ω</i>-Closed Sets and Soft <i>T</i><sub>1/2</sub> Spaces in Soft Topological Spaces |
| title_full_unstemmed | On Soft Generalized <i>ω</i>-Closed Sets and Soft <i>T</i><sub>1/2</sub> Spaces in Soft Topological Spaces |
| title_short | On Soft Generalized <i>ω</i>-Closed Sets and Soft <i>T</i><sub>1/2</sub> Spaces in Soft Topological Spaces |
| title_sort | on soft generalized i ω i closed sets and soft i t i sub 1 2 sub spaces in soft topological spaces |
| topic | soft ω-open set generalized closed sets <i>T</i><sub>1/2</sub> spaces generalized ω-closed sets soft <i>T</i><sub>1/2</sub> spaces soft generated soft topological spaces |
| url | https://www.mdpi.com/2075-1680/11/5/194 |
| work_keys_str_mv | AT sameralghour onsoftgeneralizediōiclosedsetsandsoftitisub12subspacesinsofttopologicalspaces |