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Dimension zero vs measure zero
Author(s):
Ondrej
Zindulka
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1769-1778.
MSC (1991):
Primary 28C15, 54F45;
Secondary 03E50
Posted:
September 30, 1999
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Abstract:
The following problem is discussed: If  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.
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- 4.
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Additional Information:
Ondrej
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
DOI:
10.1090/S0002-9939-99-05225-9
PII:
S 0002-9939(99)05225-9
Keywords:
Universal measure zero,
topological dimension,
zero--dimensional,
perfectly meager
Received by editor(s):
May 17, 1998
Received by editor(s) in revised form:
July 24, 1998
Posted:
September 30, 1999
Communicated by:
Alan Dow
Copyright of article:
Copyright
2000,
American Mathematical Society
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