Gowers' Ramsey Theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan

Published 19 Nov 2014 in math.LO, math.CO, and math.DS | (1411.5134v3)

Abstract: We generalize the finite version of Gowers' Ramsey theorem to multiple tetris-like operations and apply it to show that a group of homeomorphisms that preserve a "typical" linear order of branches of the Lelek fan, a compact connected metric space with many symmetries, is extremely amenable.

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