COARSE AND LIPSCHITZ UNIVERSALITY - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Fundamenta Mathematicae Année : 2021

COARSE AND LIPSCHITZ UNIVERSALITY

Florent Baudier
  • Fonction : Auteur
Pavlos Motakis
  • Fonction : Auteur
Thomas H Schlumprecht
  • Fonction : Auteur

Résumé

In this paper we provide several metric universality results. We exhibit for certain classes C of metric spaces, families of metric spaces (M i , d i) i∈I which have the property that a metric space (X, d X) in C is coarsely, resp. Lipschitzly, universal for all spaces in C if the collection of spaces (M i , d i) i∈I equi-coarsely, respectively equi-Lipschitzly, embeds into (X, d X). Such families are built as certain Schreier-type metric subsets of c 0. We deduce a metric analog to Bourgain's theorem, which generalized Szlenk's theorem, and prove that a space which is coarsely universal for all separable reflexive asymptotic-c 0 Banach spaces is coarsely universal for all separable metric spaces. One of our coarse universality results is valid under Martin's Axiom and the negation of the Continuum Hypothesis. We discuss the strength of the universality statements that can be obtained without these additional set theoretic assumptions. In the second part of the paper, we study universality properties of Kalton's interlacing graphs. In particular, we prove that every finite metric space embeds almost isometrically in some interlacing graph of large enough diameter.
Fichier principal
Vignette du fichier
BLMS_Fundamenta_revised.pdf (285.24 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03377393 , version 1 (14-10-2021)

Identifiants

Citer

Florent Baudier, Gilles Lancien, Pavlos Motakis, Thomas H Schlumprecht. COARSE AND LIPSCHITZ UNIVERSALITY. Fundamenta Mathematicae, 2021, 254 (2), pp.181-214. ⟨10.4064/fm956-9-2020⟩. ⟨hal-03377393⟩
19 Consultations
57 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More