A complete metric space without non-trivial separable Lipschitz retracts

2022/06/21 by Hájek, Petr, Quilis, Andrés
#46B20 (Primary) 46B26 #51F30 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2206.10279

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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