We recall a variation of a construction due to Laakso [3], also used by Lang and Plaut [3] of a doubling metric space 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 [6], we consider the Kuratowski embedding of into and prove that is not doubling.
Revised:
Accepted:
Published online:
Alexandros Margaris 1; James C. Robinson 1
@article{CRMATH_2020__358_4_515_0, author = {Alexandros Margaris and James C. Robinson}, title = {Some comments on {Laakso} graphs and sets of differences}, journal = {Comptes Rendus. Math\'ematique}, pages = {515--521}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {4}, year = {2020}, doi = {10.5802/crmath.70}, language = {en}, }
Alexandros Margaris; James C. Robinson. Some comments on Laakso graphs and sets of differences. Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 515-521. doi : 10.5802/crmath.70. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.70/
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