An example concerning the Menger-Urysohn formula

van Mill, Jan; Pol, Roman

doi:10.1090/S0002-9939-10-10393-1

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 $\mathbb {R}^{4}$.

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