Lattices of uniformly continuous functions determine their sublattices of bounded functions

被引:2
|
作者
Husek, Miroslav [1 ,2 ]
机构
[1] Charles Univ Prague, Prague 8, Czech Republic
[2] Purkyne Univ, Usti Nad Labem, Czech Republic
关键词
Lattice of functions; Uniform continuity;
D O I
10.1016/j.topol.2014.12.019
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
If two uniform spaces have isomorphic lattices of their uniformly continuous real-valued functions then also their sublattices of bounded functions are isomorphic. That result is used to give a different correct proof of Shirota theorem (complete metric spaces are determined by their uniformly continuous real-valued functions) than that in [1]. (C) 2014 Elsevier B.V. All rights reserved.
引用
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页码:71 / 76
页数:6
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