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

来源：

COLLOQUIUM MATHEMATICUM | 2009年 / 116卷 / 02期

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

页码：191 / 202

页数：12

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