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arXiv · 1908.02491

Some comments on Laakso graphs and sets of differences

Alexandros Margaris·James C. Robinson
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Abstract

We recall a variation of a construction due to Laakso \cite{LA}, also used by Lang and Plaut \cite{LA} of a doubling metric space $X$ that cannot be embedded into any Hilbert space. We give a more concrete version of this construction and motivated by the results of Olson \& Robinson \cite{OR}, we consider the Kuratowski embedding $\Phi(X)$ of $X$ into $L^{\infty}(X)$ and prove that $\Phi(X)-\Phi(X)$ is not doubling.

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Alexandros Margaris, James C. Robinson. 2019-08-07. Some comments on Laakso graphs and sets of differences. https://arxiv.org/abs/1908.02491

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