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

@article{OndřejZindulka2012,
abstract = { We prove that each analytic set in ℝⁿ 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. },
author = {Ondřej Zindulka},
journal = {Fundamenta Mathematicae},
keywords = {universally null; universally meager; Hausdorff dimension; upper Hausdorff dimension; Cantor cube; nearly Lipschitz mapping; monotone space},
language = {eng},
number = {2},
pages = {95-119},
title = {Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps},
url = {http://eudml.org/doc/282996},
volume = {218},
year = {2012},
}

TY - JOUR
AU - Ondřej Zindulka
TI - Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps
JO - Fundamenta Mathematicae
PY - 2012
VL - 218
IS - 2
SP - 95
EP - 119
AB - We prove that each analytic set in ℝⁿ 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.
LA - eng
KW - universally null; universally meager; Hausdorff dimension; upper Hausdorff dimension; Cantor cube; nearly Lipschitz mapping; monotone space
UR - http://eudml.org/doc/282996
ER -