Coarse and Lipschitz universality

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355103" target="_blank" >RIV/68407700:21230/21:00355103 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4064/fm956-9-2020" target="_blank" >https://doi.org/10.4064/fm956-9-2020</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4064/fm956-9-2020" target="_blank" >10.4064/fm956-9-2020</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Coarse and Lipschitz universality

Popis výsledku v původním jazyce

We provide several metric universality results. For certain classes C of metric spaces we exhibit families of metric spaces (M-i, d(i))i is an element of 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 (M-i, d(i))i is an element of 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 analogue of 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 into some interlacing graph of large enough diameter.

Název v anglickém jazyce

Coarse and Lipschitz universality

Popis výsledku anglicky

We provide several metric universality results. For certain classes C of metric spaces we exhibit families of metric spaces (M-i, d(i))i is an element of 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 (M-i, d(i))i is an element of 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 analogue of 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 into some interlacing graph of large enough diameter.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fundamenta Mathematicae

ISSN

0016-2736

e-ISSN

1730-6329

Svazek periodika

254

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

34

Strana od-do

181-214

Kód UT WoS článku

000637944900004

EID výsledku v databázi Scopus

2-s2.0-85108281593