Gowers’ Ramsey theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan. (English) Zbl 1377.05192
The reason the article appears in a combinatorial journal and is indexed under Ramsey theory is that the bulk of it is devoted to deriving a generalization of the result by W. T. Gowers [Eur. J. Comb. 13, No. 3, 141–151 (1992; Zbl 0763.46015)]. This generalization is a new Ramsey theorem which is utilized to groups which are connected with the homeomorphism group of the Lelek fan. For example, some such groups are extremely amenable, i.e., every (their) continuous action on a compact Hausdorff space admits a fixed point. The paper contains a lot of repetitions – regarding to so-called projective Fraïssé limits – from another article by the same authors [Fund. Math. 231, No. 1, 57–79 (2015; Zbl 1373.54042)].
Reviewer: Szymon Plewik (Katowice)
MSC:
| 05D10 | Ramsey theory |
References:
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