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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- by A. N. Dranishnikov
- Trans. Amer. Math. Soc. 352 (2000), 5599-5618
- DOI: https://doi.org/10.1090/S0002-9947-00-02684-2
- Published electronically: August 8, 2000
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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 $dimf(X)\cap g(Y)\leq dim(X\times Y)-n$.References
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Bibliographic 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
- MR Author ID: 212177
- Email: dranish@math.psu.edu, dranish@math.ufl.edu
- Received by editor(s): January 30, 1995
- Received by editor(s) in revised form: January 27, 1999
- Published electronically: August 8, 2000
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1781276