All Finite Sets Are Ramsey In The Maximum Norm

For two metric spaces X and Y the chromatic number x(X; Y) of X with forbidden Y is the smallest k such that there is a colouring of the points of X with k colors that contains no monochromatic copy of Y. In this article, we show that for each finite metric space M that contains at least two points the value chi (R-infinity(n); M) grows exponentially with n. We also provide explicit lower and upper bounds for some special M.