Characterizations of Convex spaces and Anti-matroids via Derived Operators
In this paper we use the notion of derived sets to study convex spaces. By axiomatizing the derived sets on convex spaces, we define c-derived operators and restricted c-derived operators. Results show that convex structures can be characterized in terms of c-derived operators. Furthermore, the link...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-05-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2019-0022 |
| _version_ | 1818690004368490496 |
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| author | Chen Fanhong Shen Chong |
| author_facet | Chen Fanhong Shen Chong |
| author_sort | Chen Fanhong |
| collection | DOAJ |
| description | In this paper we use the notion of derived sets to study convex spaces. By axiomatizing the derived sets on convex spaces, we define c-derived operators and restricted c-derived operators. Results show that convex structures can be characterized in terms of c-derived operators. Furthermore, the link between c-derived operators and Shi’s m-derived operators is studied. Specifically, it is proved that a c-derived operator is an m-derived operator if and only if it satisfies the Exchange Law. At last, we show an application of c-derived operators to anti-matroids. |
| first_indexed | 2024-12-17T12:19:06Z |
| format | Article |
| id | doaj.art-00ecf598ba8645c68eebe7c5996f32a4 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T12:19:06Z |
| publishDate | 2019-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-00ecf598ba8645c68eebe7c5996f32a42022-12-21T21:49:02ZengDe GruyterOpen Mathematics2391-54552019-05-0117133134210.1515/math-2019-0022math-2019-0022Characterizations of Convex spaces and Anti-matroids via Derived OperatorsChen Fanhong0Shen Chong1School of Civil Engineering and Architecture, Yanching Institute of Technology, Hebei, 065201, ChinaBeijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Fangshan District, Beijing, 100081, ChinaIn this paper we use the notion of derived sets to study convex spaces. By axiomatizing the derived sets on convex spaces, we define c-derived operators and restricted c-derived operators. Results show that convex structures can be characterized in terms of c-derived operators. Furthermore, the link between c-derived operators and Shi’s m-derived operators is studied. Specifically, it is proved that a c-derived operator is an m-derived operator if and only if it satisfies the Exchange Law. At last, we show an application of c-derived operators to anti-matroids.https://doi.org/10.1515/math-2019-0022convex spacederived operatorm-derived operatormatroidanti-matroid52a0114p25 |
| spellingShingle | Chen Fanhong Shen Chong Characterizations of Convex spaces and Anti-matroids via Derived Operators Open Mathematics convex space derived operator m-derived operator matroid anti-matroid 52a01 14p25 |
| title | Characterizations of Convex spaces and Anti-matroids via Derived Operators |
| title_full | Characterizations of Convex spaces and Anti-matroids via Derived Operators |
| title_fullStr | Characterizations of Convex spaces and Anti-matroids via Derived Operators |
| title_full_unstemmed | Characterizations of Convex spaces and Anti-matroids via Derived Operators |
| title_short | Characterizations of Convex spaces and Anti-matroids via Derived Operators |
| title_sort | characterizations of convex spaces and anti matroids via derived operators |
| topic | convex space derived operator m-derived operator matroid anti-matroid 52a01 14p25 |
| url | https://doi.org/10.1515/math-2019-0022 |
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