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The metric geometry of the Hamming cube and applications

Florent Baudier, Daniel Freeman, Thomas Schlumprecht and András Zsák

Geometry & Topology 20 (2016) 1427–1444

The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an application, the first nontrivial lower bounds on the C(K)–distortion of important classes of separable Banach spaces, where K is a countable compact space in the family {[0,ω],[0,ω 2],,[0,ω2],,[0,ωk n],,[0,ωω]} are obtained.

In memory of Luis Sánchez-González

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countable compact metric space, bi-Lipschitz embedding, $C(K)$ space
Mathematical Subject Classification 2010
Primary: 46B20, 46B80
Secondary: 46B85
Received: 21 March 2014
Revised: 31 May 2015
Accepted: 10 July 2015
Published: 4 July 2016
Proposed: Bruce Kleiner
Seconded: Tobias H Colding, Dmitri Burago
Florent Baudier
Department of Mathematics
Texas A&M University
College Station, TX 77843
Institut de Mathématiques Jussieu-Paris Rive Gauche
Université Pierre et Marie Curie
75005 Paris
Daniel Freeman
Department of Mathematics and Computer Science
Saint Louis University
220 N. Grand Blvd.
St. Louis, MO 63103
Thomas Schlumprecht
Department of Mathematics
Texas A&M University
College Station, TX 77843
Faculty of Electrical Engineering
Czech Technical University in Prague
Zikova 4
166 27 Prague
Czech Republic
András Zsák
University of Cambridge
Cambridge CB2 1RD