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

• Autorzy: Ondřej Zindulka
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54E35: Metric spaces, metrizability
• 28A78: Hausdorff and packing measures
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 218
• Numer: 2
• Strony: 95-119

Daty

wydano

2012

Twórcy

autor

Ondřej Zindulka

• Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 160 00 Praha 6, Czech Republic

Identyfikatory

DOI

10.4064/fm218-2-1