All finite sets are Ramsey in the maximum norm

  title={All finite sets are Ramsey in the maximum norm},
  author={Andrey B. Kupavskii and A. A. Sagdeev},
  journal={Forum of Mathematics, Sigma},
Abstract For two metric spaces $\mathbb X$ and $\mathcal Y$ the chromatic number $\chi ({{\mathbb X}};{{\mathcal{Y}}})$ of $\mathbb X$ with forbidden $\mathcal Y$ is the smallest k such that there is a colouring of the points of $\mathbb X$ with k colors that contains no monochromatic copy of $\mathcal Y$. In this article, we show that for each finite metric space $\mathcal {M}$ that contains at least two points the value $\chi \left ({{\mathbb R}}^n_\infty; \mathcal M \right )$ grows… 
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