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

Dranishnikov, A.

doi:10.1090/S0002-9947-00-02684-2

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 and , both with dimension at most , 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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