可数仿紧空间和可数中紧空间的函数刻画

Function Characterizations of Countably Paracompact Space and Countably Mesocompact

利用半连续函数给出对可数仿紧空间和可数中紧空间的若干等价刻画,主要结论为:X为可数仿紧空间当且仅当对任一递减的函数列{fn∈U(X):n∈N}且fn→0,存在函数列{gn∈L(X):n∈N}和{hn∈U(X):n∈N},使得对每一n∈N,fn≤gn≤hn且hn→0;X为可数中紧空间当且仅当对X上的每一上半连续函数f,存在下半连续且k-上有界函数φ(f),使得f≤φ(f)。

Some characterizations of countably paracompact spaces and countably mesocompact spaces,were given with semi-continuous funtions.The main results are as follows.X is a countably paracompact if and only if for every decreasing sequences{gn∈L(X):n∈N}and{hn∈U(X):n∈N}of functions such that for each n∈N fn≤gn≤hn and hn→0.X is a countably mesocompact if and only if for each upper semi-continuous function f,there exists a lower semi-continuous and k-upper bounded functionφ(f),such that f≤φ(f).