逼近辅助关系与伪测度拓扑

Approximating Auxiliary Relations and the Pseudo-measurement Topology

在具有辅助关系的偏序集上引入伪测度拓扑,研究其性质以及与其它内蕴拓扑的关系。主要结果有:(1)具有逼近辅助关系的偏序集上的伪测度拓扑是零维的;(2)具有辅助关系的偏序集有可数辅助基当且仅当其上的伪测度拓扑是可分的;(3)具有逼近辅助关系的偏序集是可数集当且仅当其上的伪测度拓扑是可分可度量化的。

The new concept of the pseudo-measurement topology on posets with auxiliary relations is introduced. Some basic properties of the pseudo-measurement topology and relations with other intrinsic topologies are given. The main results are： （1） the pseudo-measurement topology on a poset with an approximating auxiliary relation is zero-d{mensional; （2） a poser with an auxiliary relation has a countable auxiliary basis iff its pseudo-measurement topology is separable; （3） a poset with an approximating auxiliary relation is countable iff its pseudo-measurement topology is separable and metrizable.