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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Dimension of subsets of product spaces


Author: Y. Sternfeld
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
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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 [Enhancements On Off] (What's this?)

  • [1] C. F. K. Jung, Mappings on compact metric spaces, Colloq. Math. 19 (1968), 73-76. MR 0229215 (37:4789)
  • [2] J. Keesling, Closed mappings which lower dimension, Colloq. Math. 20 (1969), 237-241. MR 0248768 (40:2019)
  • [3] A. Lelek, Dimension inequalities for unions and mappings of separable metric spaces, Colloq. Math. 23 (1971), 69-91. MR 0322829 (48:1190)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0612738-X
Article copyright: © Copyright 1981 American Mathematical Society

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