抽象基上的伪e拓扑与伪ρ拓扑

The Pseudo e-topology and the Pseudo ρ-topology on Abstract Bases

在抽象基上引入了伪e拓扑和伪ρ拓扑,研究了这两种内蕴拓扑的性质以及与其它内蕴拓扑的关系。利用伪e拓扑与伪ρ拓扑得到具有辅助关系的偏序集的辅助基的若干等价刻画。证明了具有辅助关系的偏序集的辅助基恰是伪ρ拓扑的稠子集。

The new concepts of the pseudo e-topology and the pseudo ρ-topology on abstract bases are introduced. Some basic properties of the pseudo e-topology and the pseudo ρ-topology and relations with other intrinsic topologies are explored. Via the pseudo e-topology and the pseudo ρ-topology, we obtain several characterizations of auxiliary bases of posets with auxiliary relations. It is proved that, in posets with auxiliary relations, auxiliary bases correspond exactly to dense sets with respect to the pseudo ρ-topology.