Dimension of subsets of product spaces
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- by Y. Sternfeld
- Proc. Amer. Math. Soc. 82 (1981), 452-454
- DOI: https://doi.org/10.1090/S0002-9939-1981-0612738-X
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Abstract:
It is proved that under a certain condition on a separable metric space $X$, each compact subset $W$ of $X \times Y$ with $\dim W = \dim X + \dim Y$ contains a product $X’ \times Y’ \subset W$ with $\dim X’ = \dim X$ and $\dim Y’ = \dim Y$. This condition is satisfied when $X$ is a Euclidean space.References
- Calvin F. K. Jung, Mappings on compact metric spaces, Colloq. Math. 19 (1968), 73–76. MR 229215, DOI 10.4064/cm-19-1-73-76
- James Keesling, Closed mappings which lower dimension, Colloq. Math. 20 (1969), 237–241. MR 248768, DOI 10.4064/cm-20-2-237-241
- A. Lelek, Dimension inequalities for unions and mappings of separable metric spaces, Colloq. Math. 23 (1971), 69–91. MR 322829, DOI 10.4064/cm-23-1-69-91
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 452-454
- MSC: Primary 54F45; Secondary 54B10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0612738-X
- MathSciNet review: 612738