A complete metric space without non-trivial separable Lipschitz retracts
Functional Analysis
2022-06-22 v1 Metric Geometry
Abstract
We construct a complete metric space of cardinality continuum such that every non-singleton closed separable subset of fails to be a Lipschitz retract of . 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.
Keywords
Cite
@article{arxiv.2206.10279,
title = {A complete metric space without non-trivial separable Lipschitz retracts},
author = {Petr Hájek and Andrés Quilis},
journal= {arXiv preprint arXiv:2206.10279},
year = {2022}
}
Comments
42 pages, 9 figures