ON CONTINUOUS EXTENSION OF UNIFORMLY CONTINUOUS FUNCTIONS AND METRICS

被引:6
|
作者
Banakh, T. [1 ]
Brodskiy, N. [2 ]
Stasyuk, I. [1 ]
Tymchatyn, E. D. [3 ]
机构
[1] Lviv Natl Univ, Dept Mech & Math, UA-79000 Lvov, Ukraine
[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA
[3] Univ Saskatchewan, Dept Math & Stat, Saskatoon, SK S7N 5E6, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
extension operator; modulus function; continuity;
D O I
10.4064/cm116-2-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove that there exists a continuous regular, positive homogeneous extension operator for the family of all uniformly continuous bounded real-valued functions whose domains are closed subsets of a bounded metric space (X, d). In particular, this operator preserves Lipschitz functions. A similar result is obtained for partial metrics and ultrametrics.
引用
收藏
页码:191 / 202
页数:12
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