由邻域导出的拟阵结构

Matroidal Structure Induced by Neighborhood

通过利用覆盖的邻域和补邻域构造了一个集族,并且证明其满足拟阵的独立集公理,从而建立了一种拟阵结构,并且对这种拟阵的相关集、极小圈、秩函数和闭包等表达形式进行了研究。最后,给出了此类拟阵的对偶拟阵的独立集、极小圈的等价刻画。

This paper constructed a matroidal structure by the neighborhood of a covering.At first,a family of sets was constructed through neighborhood and complementary neighborhood on a covering and the family of sets was proved to satisfy independent set axioms.Thus a matroidal structure of a covering was established.Then,we investigated some characteristics of this kind of matroid,such as dependent set,circuit,rank function and closure.At last,we gave some equivalent characterizations of dual matroid of the matroid,such as independent set and cicuit.