Cantor sets of low density and Lipschitz functions on C1 curves

Chiclana, Rafael

doi:10.1016/j.jmaa.2022.126489

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2023

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Cited by 3 publications

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“…In the past few years, this topic has been intensively studied. We send the reader to [1,2,3,4,5,6,7,11,12,14,15,17,18,19] and the references therein.…”

Section: Preliminaries and Notationmentioning

confidence: 99%

On isometric embeddings into the set of strongly norm-attaining Lipschitz functions

Dantas¹,

Medina²,

Quilis³

et al. 2022

Preprint

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In this paper, we provide an infinite metric space M such that the set SNA(M ) of strongly norm-attaining Lipschitz functions does not contain a subspace which is isometric to c 0 . This answers a question posed by Antonio Avilés, Gonzalo Martínez Cervantes, Abraham Rueda Zoca, and Pedro Tradacete. On the other hand, we prove that SNA(M ) contains an isometric copy of c 0 whenever M is a metric space which is not uniformly discrete. In particular, the latter holds true for infinite compact metric spaces while it does not for proper metric spaces. Some positive results in the non-separable setting are also given.

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“…In the past few years, this topic has been intensively studied. We send the reader to [1,2,3,4,5,6,7,11,12,14,15,17,18,19] and the references therein.…”

Section: Preliminaries and Notationmentioning

confidence: 99%