The metric geometry of the Hamming cube and applications

Florent Baudier, Daniel Freeman, Thomas Schlumprecht, András Zsák
2016 Geometry and Topology  
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,\omega],[0,\omega\cdot 2],\dots, [0,\omega^2], \dots, [0,\omega^k\cdot
more » ... ot n],\dots,[0,\omega^\omega]\}\ ,$ are obtained.
doi:10.2140/gt.2016.20.1427 fatcat:4buhznhnmfazjbz3wap3lqim3y