Nguyen Van Thé, Lionel
Fixed points in compactifications and combinatorial counterparts
Annales Henri Lebesgue, Volume 2  (2019), p. 149-185

KeywordsRamsey theory, fixed point properties in topological dynamics

### Abstract

The Kechris–Pestov–Todorcevic correspondence connects extreme amenability of topological groups with Ramsey properties of classes of finite structures. The purpose of the present paper is to recast it as one of the instances of a more general construction, allowing to show that Ramsey-type statements actually appear as natural combinatorial expressions of the existence of fixed points in certain compactifications of groups, and that similar correspondences in fact exist in various dynamical contexts.

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