Lipschitz-free spaces over strongly countable-dimensional spaces and approximation properties

2024/05/30 by Talimdjioski, Filip · 1 citation
#46B28 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B20

paper · doi:10.48550/arxiv.2405.19800

Abstract

Let T be a compact, metrisable and strongly countable-dimensional topological space. Let M^T be the set of all metrics d on T compatible with its topology, and equip M^T with the topology of uniform convergence, where the metrics are regarded as functions on T². We prove that the set A^T,1 of metrics d\inM^T for which the Lipschitz-free space F(T,d) has the metric approximation property is residual in M^T.

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• Lipschitz-free spaces and Bossard's reduction argument

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