Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations
In rough set theory, there are many covering approximation spaces, so how to classify covering approximation spaces has become a hot issue. In this paper, we propose the concepts of a covering approximation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display=&...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-09-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/10/1808 |
| _version_ | 1797572247930535936 |
|---|---|
| author | Xiao Shang Pei Wang Ronghuo Wu Hanyu E |
| author_facet | Xiao Shang Pei Wang Ronghuo Wu Hanyu E |
| author_sort | Xiao Shang |
| collection | DOAJ |
| description | In rough set theory, there are many covering approximation spaces, so how to classify covering approximation spaces has become a hot issue. In this paper, we propose the concepts of a covering approximation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>1</mn></msub></semantics></math></inline-formula>-space, <i>F</i>-symmetry, covering rough continuous mapping, and covering rough homeomorphism mapping, and we obtain some interesting results. We have used the above definitions and results to classify covering approximation spaces. Finally, we find a new method for constructing topologies, obtain some properties, and provide an example to illustrate our method’s similarities and differences with other construction methods. |
| first_indexed | 2024-03-10T20:51:41Z |
| format | Article |
| id | doaj.art-4561c0f65a894fd0b8c0dc41ba65a0f8 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:51:41Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4561c0f65a894fd0b8c0dc41ba65a0f82023-11-19T18:17:01ZengMDPI AGSymmetry2073-89942023-09-011510180810.3390/sym15101808Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering RelationsXiao Shang0Pei Wang1Ronghuo Wu2Hanyu E3Center for Applied Mathematics of Guangxi, Yulin Normal University, Yulin 537000, ChinaCenter for Applied Mathematics of Guangxi, Yulin Normal University, Yulin 537000, ChinaCenter for Applied Mathematics of Guangxi, Yulin Normal University, Yulin 537000, ChinaDepartment of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 1H9, CanadaIn rough set theory, there are many covering approximation spaces, so how to classify covering approximation spaces has become a hot issue. In this paper, we propose the concepts of a covering approximation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>1</mn></msub></semantics></math></inline-formula>-space, <i>F</i>-symmetry, covering rough continuous mapping, and covering rough homeomorphism mapping, and we obtain some interesting results. We have used the above definitions and results to classify covering approximation spaces. Finally, we find a new method for constructing topologies, obtain some properties, and provide an example to illustrate our method’s similarities and differences with other construction methods.https://www.mdpi.com/2073-8994/15/10/1808covering approximation spacecovering rough continuous mappingrelationtopology |
| spellingShingle | Xiao Shang Pei Wang Ronghuo Wu Hanyu E Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations Symmetry covering approximation space covering rough continuous mapping relation topology |
| title | Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations |
| title_full | Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations |
| title_fullStr | Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations |
| title_full_unstemmed | Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations |
| title_short | Continuous Mapping of Covering Approximation Spaces and Topologies Induced by Arbitrary Covering Relations |
| title_sort | continuous mapping of covering approximation spaces and topologies induced by arbitrary covering relations |
| topic | covering approximation space covering rough continuous mapping relation topology |
| url | https://www.mdpi.com/2073-8994/15/10/1808 |
| work_keys_str_mv | AT xiaoshang continuousmappingofcoveringapproximationspacesandtopologiesinducedbyarbitrarycoveringrelations AT peiwang continuousmappingofcoveringapproximationspacesandtopologiesinducedbyarbitrarycoveringrelations AT ronghuowu continuousmappingofcoveringapproximationspacesandtopologiesinducedbyarbitrarycoveringrelations AT hanyue continuousmappingofcoveringapproximationspacesandtopologiesinducedbyarbitrarycoveringrelations |