An example concerning the Menger-Urysohn formula
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- by Jan van Mill and Roman Pol PDF
- Proc. Amer. Math. Soc. 138 (2010), 3749-3752 Request permission
Abstract:
We construct subsets $A$, $B$ of the Euclidean space $\mathbb {R}^{4}$ such that $\hbox {dim}(A\cup B)>\hbox {dim}(A \times B)+1$. This provides a counterexample to a conjecture by E. Ščepin for subspaces of $\mathbb {R}^{4}$.References
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Additional Information
- Jan van Mill
- Affiliation: Department of Mathematics, Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
- MR Author ID: 124825
- Email: vanmill@few.vu.nl
- Roman Pol
- Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
- Email: r.pol@mimuw.edu.pl
- Received by editor(s): August 7, 2009
- Received by editor(s) in revised form: January 12, 2010
- Published electronically: May 6, 2010
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 3749-3752
- MSC (2010): Primary 54F45, 55M10
- DOI: https://doi.org/10.1090/S0002-9939-10-10393-1
- MathSciNet review: 2661573