S_ω×X的k空间性质及相关结果

k-Space Property of S_ω×X and Related Results

本文讨论了特殊的度量空间Tω和Tω1在探讨具有点可数k网的k空间类中乘积性质与映射性质方面的作用．一方面,通过Tω分析了为解决1973年Michael提出的“k空间的乘积问题”而引入的三个空间类的相互关系;另一方面,利用Tω1研究了局部可分度量空间的闭映象的内在刻画．

In this paper some functions of product and mapping properties of k-spaces with a point-countable k-network are discussed via special metric spaces Tω and Tω1. The relationships among the three classes of spaces, which are introduced respectively for solving the ＂the products of k-spaces question＂ posed by Michael in 1973, are analysed via Tω; on the other hand, some internal characterizations of closed images of locally separable metric spaces are studied via Tω1.