Characterizations of Convex spaces and Anti-matroids via Derived Operators

Abstract

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.

Keywords

• convex space
• derived operator
• m-derived operator
• matroid
• anti-matroid
• 52a01
• 14p25