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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An example concerning the Menger-Urysohn formula


Authors: Jan van Mill and Roman Pol
Journal: Proc. Amer. Math. Soc. 138 (2010), 3749-3752
MSC (2010): Primary 54F45, 55M10
Published electronically: May 6, 2010
MathSciNet review: 2661573
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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}$.


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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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10393-1
PII: S 0002-9939(10)10393-1
Keywords: Menger-Urysohn formula, dimension, weakly $n$-dimensional, dimension of product
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.