An infinite-dimensional version of Gowers' \FIN_{\± k}\n theorem

2019/05/06 by Jamal K. Kawach, Kawach, Jamal K.
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1905.02160

openalex publication_date 2019/05/06 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We prove an infinite-dimensional version of an approximate Ramsey theorem of\nGowers, initially used to show that every Lipschitz function on the unit sphere\nof c₀ is oscillation stable. To do so, we use the theory of ultra-Ramsey\nspaces developed by Todorcevic in order to obtain an Ellentuck-type theorem for\nthe space of all infinite block sequences in \FIN_{\± k}.\n

Related

• Parametrized Ramsey theory of infinite block sequences of vectors
• Another proof of a Gowers theorem
• Finite forms of Gowers' Theorem on the oscillation stability of c₀
• Big Ramsey degrees in the metric setting
• Oscillation stability by the Carlson-Simpson theorem