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 |
| Summary: | 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. |
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| ISSN: | 2391-5455 |