L-拟序集上的广义Alexandroff拓扑与广义超度量空间上的广义Alexandroff拓扑

Generalized Alexandroff Topologies on L-Quasi-Ordered-Sets and Generalized Alexandroff Topologies on Generalized Ultrametric Spaces

证明 [1 0 ]中定义的 L -拟序集上的广义 Alexandroff拓扑是 [2 ]中定义的广义超度量空间上的广义 Alexandroff拓扑的推广 ,并且广义超度量空间中有关广义 Alexandroff拓扑的许多性质都可以推广到 L

In this paper, it is proved that generalized Alexandroff topologies on L-quasi-ordered sets are generalizations of generalized Alexandroff topologies on generalized ultrametric spaces, and (many properties) about generalized Alexandroff topologies on generalized ultrametric spaces can be (generalized) to L-quasi-ordered sets.