L-拟序集上的广义Alexandroff拓扑

Generalized Alexandroff Topologies on L-Quasi Ordered Sets

在一类特殊的 L -拟序集上定义广义 Alexandroff拓扑 ,限制到通常的拟序集上就是 Alexandroff拓扑 ,并且该拓扑可以由其上的一族 Alexandroff拓扑取并得到。还证明任意一个拓扑空间的拓扑都可以表示为某个 L-拟序集上的广义 Alexandroff拓扑。

In this paper,the generalized Alexandroff topology on an L-quasi ordered set is constructed, where L denotes a completely distributive lattice in which 1 is a molecule, it is exactly an Alexandroff topology when restricted to the ordinary quasi ordered set.It is proved that the generalized Alexandroff topology on an L-quasi ordered set (X,e) can be obtained by the join of a family of the Alexandroff topologies on X, and a topology on any topological space can be represented as a generalized Alexandroff topology on an L-quasi ordered set.