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arXiv · 2206.10279

A complete metric space without non-trivial separable Lipschitz retracts

Petr Hájek·Andrés Quilis
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Abstract

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.

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Petr Hájek, Andrés Quilis. 2022-06-21. A complete metric space without non-trivial separable Lipschitz retracts. https://arxiv.org/abs/2206.10279

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