斯米尔诺夫度量化定理的一个应用

李孝传教授曾证明:(X,d)是度量空间,d与d’是拓扑相同的,(X,d)满足B_*-公理(X,(d’)是可分的。并研究了一系列有关B_*-公理的命题。本文用著名的斯米尔诺夫度量化定理,对不满足B_*-公理的空间作一单点扩张,证明其可度量化。从而得到非B_*-公理的空间的一个新的性质。

AN APPLICATION-OF NAGATA-SMIRNOV METRIZATION THEOREM

The B_*-axicm is introduced by professor Li Xiaochuan. Many studies on the B_*-axiom are made by him. Especially, he proves that if (X,d) is a metric space, d and d' are topology-equivalent, then in (X,d) B_*-axiom is true (?)(X,d') is a separable space. In this paper, the famous Nagata-Smirnov metrization theorem is employed to a metric space in which B_*-axiom is nontrue to make a one-point extension, and the extensional space is proved to be metrizable space.