A complete metric space without non-trivial separable Lipschitz retracts

被引：3
作者：
Hajek, Petr [1 ]
Quilis, Andres [1 ,2 ]
机构：
[1] Czech Tech Univ, Fac Elect Engn, Dept Math, Technicka 2, Prague 6, Czech Republic
[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Camino Vera S-N, Valencia 46022, Spain
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2023年 / 285卷 / 02期
关键词：
Lipschitz retractions; FREE BANACH-SPACES; COMPLEMENTED SUBSPACES; UNIFORM;
D O I：
10.1016/j.jfa.2023.109941
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct a complete metric space M of cardinality continuum such that every non-singleton closed separable subset of M fails to be a Lipschitz retract of M. This provides a metric analogue to the various classical and recent examples of Banach spaces failing to have linearly complemented subspaces of prescribed smaller density character. (c) 2023 Elsevier Inc. All rights reserved.
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页数：41
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