Mapping analytic sets onto cubes by little Lipschitz functions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03

AUTHORS

Jan Malý, Ondřej Zindulka

ABSTRACT

A mapping f:X→Y between metric spaces is called little Lipschitz if the quantity lipf(x)=lim infr→0diamf(B(x,r))ris finite for every x∈X. We prove that if a compact (or, more generally, analytic) metric space has packing dimension greater than n, then it can be mapped onto an n-dimensional cube by a little Lipschitz function. The result requires two facts that are interesting in their own right. First, an analytic metric space X contains, for any ε>0, a compact subset S that embeds into an ultrametric space by a Lipschitz map, and . Second, a little Lipschitz function on a closed subset admits a little Lipschitz extension. More... »

PAGES

91-105

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s40879-018-0288-z

DOI

http://dx.doi.org/10.1007/s40879-018-0288-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107301822


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