Coarse and Lipschitz universality
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Coarse and Lipschitz universality
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fundamenta Mathematicae
ISSN
0016-2736
e-ISSN
1730-6329
Volume of the periodical
254
Issue of the periodical within the volume
2
Country of publishing house
PL - POLAND
Number of pages
34
Pages from-to
181-214
UT code for WoS article
000637944900004
EID of the result in the Scopus database
2-s2.0-85108281593