Some comments on Laakso graphs and sets of differences

2019/08/07 by Margaris, Alexandros, Robinson, James C.
#FOS: Mathematics #General Topology (math.GN) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1908.02491

Abstract

We recall a variation of a construction due to Laakso \citeLA, also used by Lang and Plaut \citeLA 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 \citeOR, we consider the Kuratowski embedding Φ(X) of X into L^∞(X) and prove that Φ(X)-Φ(X) is not doubling.

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