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arXiv · 2309.17274

A Ramsey-type phenomenon in two and three dimensional simplices

Sumun Iyer
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Abstract

We develop a Ramsey-like theorem for subsets of the two and three-dimensional simplex. A generalization of the combinatorial theorem presented here to all dimensions would produce a new proof that $\textrm{Homeo}_+[0,1]$ is extremely amenable (a theorem due to Pestov) using general results of Uspenskij on extreme amenability in homeomorphism groups.

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Sumun Iyer. 2023-09-29. A Ramsey-type phenomenon in two and three dimensional simplices. https://arxiv.org/abs/2309.17274

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