Constructions in topological dynamics via ultrafilters
Dana Bartošová

Given a topological group G, I will show how one can construct two basic dynamical systems for G - the greatest ambit and the universal minimal flow - as spaces of (near) ultrafilters on G. So far this proved to be especially useful in the case G is a group of automorphisms of a first order structure, where an equivalence was established between structural Ramsey theory + and extreme amenability of groups (fixed point on compacta property) by Kechris, Pestov and Todorcevic.


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