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On the dimension of the product of two compacta and the dimension of their intersection in general position in Euclidean space


Author: A. N. Dranishnikov
Journal: Trans. Amer. Math. Soc. 352 (2000), 5599-5618
MSC (2000): Primary 55M10, 55N45
DOI: https://doi.org/10.1090/S0002-9947-00-02684-2
Published electronically: August 8, 2000
MathSciNet review: 1781276
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Abstract:

For every two compact metric spaces $X$ and $Y$, both with dimension at most $n-3$, there are dense $G_{\delta}$-subsets of mappings $f:X \to \mathbb{R}^n$ and $g:Y\to \mathbb{R}^n$ with $dimf(X)\cap g(Y)\leq dim(X\times Y)-n$.


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Additional Information

A. N. Dranishnikov
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Address at time of publication: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: dranish@math.psu.edu, dranish@math.ufl.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02684-2
Received by editor(s): January 30, 1995
Received by editor(s) in revised form: January 27, 1999
Published electronically: August 8, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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