Dimension zero vs measure zero
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- by Ondřej Zindulka PDF
- Proc. Amer. Math. Soc. 128 (2000), 1769-1778 Request permission
Abstract:
The following problem is discussed: If $X$ is a topological space of universal measure zero, does it have also dimension zero? It is shown that in a model of set theory it is so for separable metric spaces and that under the Martin’s Axiom there are separable metric spaces of positive dimension yet of universal measure zero. It is also shown that for each finite measure in a metric space there is a zero–dimensional subspace that has full measure. Similar questions concerning perfectly meager sets and other types of small sets are also discussed.References
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Additional Information
- Ondřej Zindulka
- Affiliation: Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 160 00 Prague 6, Czech Republic
- Email: zindulka@mat.fsv.cvut.cz
- Received by editor(s): May 17, 1998
- Received by editor(s) in revised form: July 24, 1998
- Published electronically: September 30, 1999
- Communicated by: Alan Dow
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1769-1778
- MSC (1991): Primary 28C15, 54F45; Secondary 03E50
- DOI: https://doi.org/10.1090/S0002-9939-99-05225-9
- MathSciNet review: 1646213