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The
metric geometry of the Hamming cube and applications
Florent Baudier, Daniel Freeman, Thomas Schlumprecht and András Zsák |
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Geometry & Topology 20 (2016) 1427–1444
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Abstract |
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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 –distortion of important classes of separable Banach spaces, where is a countable compact space in the family are obtained. |
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In memory of Luis Sánchez-González |
Keywords
countable compact metric space, bi-Lipschitz embedding,
$C(K)$ space
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Mathematical Subject Classification 2010
Primary: 46B20, 46B80
Secondary: 46B85
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References |
Publication
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
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Authors |
| Florent Baudier | |
| Department of Mathematics Texas A&M University College Station, TX 77843 USA |
Institut de Mathématiques
Jussieu-Paris Rive Gauche Université Pierre et Marie Curie 75005 Paris France |
| Daniel Freeman | |
| Department of Mathematics and
Computer Science Saint Louis University 220 N. Grand Blvd. St. Louis, MO 63103 USA |
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| Thomas Schlumprecht | |
| Department of Mathematics Texas A&M University College Station, TX 77843 USA |
Faculty of Electrical
Engineering Czech Technical University in Prague Zikova 4 166 27 Prague Czech Republic |
| András Zsák | |
| Peterhouse University of Cambridge Cambridge CB2 1RD UK |
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