Hausdorff dimension of metric spaces and Lipschitz maps onto cubes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F14%3A00241236" target="_blank" >RIV/68407700:21110/14:00241236 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1093/imrn/rns223" target="_blank" >http://dx.doi.org/10.1093/imrn/rns223</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rns223" target="_blank" >10.1093/imrn/rns223</a>
Alternative languages
Result language
angličtina
Original language name
Hausdorff dimension of metric spaces and Lipschitz maps onto cubes
Original language description
We prove that a compact metric space (ormore generally an analytic subset of a complete separable metric space) of Hausdorff dimension bigger than k can always be mapped onto a k-dimensional cube by a Lipschitz map. We also show that this does not hold for arbitrary separable metric spaces. As an application, we essentially answer a question of Urbanski.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Mathematics Research Notices
ISSN
1073-7928
e-ISSN
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Volume of the periodical
2014
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
14
Pages from-to
289-302
UT code for WoS article
000330445600001
EID of the result in the Scopus database
2-s2.0-84892779218