Local and global continuous ε-selection

被引：16
|
作者：
Tsar'kov, I. G. [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Moscow, Russia
来源：
IZVESTIYA MATHEMATICS | 2016年 / 80卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
epsilon-selection; monotone path-connected sets; delta-solarity; B-infinite connectedness; B-approximative infinite connectedness; moduli of approximative continuity; BANACH-SPACES; SETS; APPROXIMATION; OPERATOR; SPLINES;
D O I：
10.1070/IM8348
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study properties of sets for which there is a continuous selection from the set of almost-best approximants. We establish relations between local and global selections, give various examples of sets possessing a continuous epsilon-selection, and introduce the notions of moduli of approximative continuity, approximative delta-solarity and uniform approximative continuity. These notions enable us to establish the delta-solarity of sets under certain conditions.
引用
收藏
页码：442 / 461
页数：20
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