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Another proof of a Gowers theorem | Jesús E. Nieto
; | Date: |
27 Sep 2012 | Abstract: | W. T. Gowers proved that every Lipschitz function from the unit sphere of the
Banach space $c_0$ to $mathbb{R}$ is oscilation stable. His proof uses a
result about finite partitions of the set $FIN_k$ of finitely supported
functions $p$ from $mathbb{N}$ to ${0,1,...,k}$ with $k$ in $Im(p)$. Every
known proof of this fact uses methods of topological dynamics on the space
$etamathbb{N}$ of ultrafilters on $mathbb{N}$. We give a purely
combinatorial proof of this result avoiding the use of ultrafilters. | Source: | arXiv, 1209.6103 | Services: | Forum | Review | PDF | Favorites |
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