TIETZE EXTENSIONS AND CONTINUOUS-SELECTIONS FOR METRIC PROJECTIONS

被引：1
|
作者：
DEUTSCH, F
LI, W
PARK, SH
机构：
[1] Department of Mathematics, Pennsylvania State University, University Park
来源：
JOURNAL OF APPROXIMATION THEORY | 1991年 / 64卷 / 01期
关键词：
D O I：
10.1016/0021-9045(91)90086-P
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
There is an intimate relationship between (1) the set of all Tietze extensions of a given continuous function on a compact subset S of a locally compact Hausdorff space T to all of T, and (2) the set of all best approximations to elements of C0(T) from the ideal M in C0(T) consisting of those functions which vanish on S. This relation is used, for example, to deduce that the Tietze extension map has a linear selection if and only if the metric projection onto M has a linear selection. It is known that the former holds whenever T is metrizable. © 1991.
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页码：55 / 68
页数：14
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