Some uniformities on X related to topological properties of C(X)

被引：2
|
作者：
Carlos Ferrando, Juan [1 ]
机构：
[1] Univ Miguel Hernandez, Ctr Invest Operat, Elche 03202, Spain
来源：
TOPOLOGY AND ITS APPLICATIONS | 2014年 / 172卷
关键词：
Uniform space; Trans-separable space; Web-compact space; DCCC property; POINTWISE COMPACTNESS;
D O I：
10.1016/j.topol.2014.05.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
If X is a Hausdorff completely regular space, we characterize those spaces C-c(X) whose compact sets are metrizable in terms of a particular uniformity on X. This fact is used to show that for a k-space X are equivalent (i) X satisfies the discrete countable chain condition, (ii) every admissible uniformity on X is trans-separable, and (iii) every compact set of C-c(X) is metrizable. Several examples examine this result. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：41 / 46
页数：6
相关论文
共 50 条
12345