某些具有紧-Gδ性质的空间的函数刻画

Function Characterizations of Some Spaces with Compact Gδ-Property

实值函数是刻画某些拓扑空间的有用工具,许多空间类都可以用满足一定条件的实值函数刻画,如:层空间、k-半层空间等。本文利用实值函数给出了某些具有紧-Gδ性质的空间的函数刻画,如:γ-空间、c-层空间、kc-半层空间等,推广了已有文献中关于层空间,k-半层空间等的一些结果。

Real-valued functions are useful tools for the characterizations of some topological spaces. Many classes of spaces can be characterized with real-valued functions that satisfy certain conditions, such as stratifiable spaces, k-semi-stratifiable spaces, etc. In this paper, we present some charac-terizations of spaces with compact Gδ-property in terms of real-valued functions, such as γ-spaces, c-stratifiable spaces, kc-stratifiable spaces, etc. The results obtained generalize some corresponding results for stratifiable spaces, k-semi-stratifiable spaces in the literature.