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
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Trans. Amer. Math. Soc. 352 (2000), 5599-5618 Request permission

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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