Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps.

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F12%3A00203412" target="_blank" >RIV/68407700:21110/12:00203412 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4064/fm218-2-1" target="_blank" >http://dx.doi.org/10.4064/fm218-2-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4064/fm218-2-1" target="_blank" >10.4064/fm218-2-1</a>

Result language

angličtina

Original language name

Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps.

Original language description

We prove that each analytic set contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitz-like mappings of separable metric spaces onto Cantor cubes and self-similar sets.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2012

Confidentiality

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

Name of the periodical

Fundamenta Mathematicae

ISSN

0016-2736

e-ISSN

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Volume of the periodical

218

Issue of the periodical within the volume

2

Country of publishing house

PL - POLAND

Number of pages

25

Pages from-to

95-119

UT code for WoS article

000310111200001

EID of the result in the Scopus database

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