Ramsey-type results for metric spaces (Q579261)

The author proves the following ``Ramsey type'' theorem for metric spaces: ``If X, a metric space, is either finite, or the one consisting of the points \(\{x_ i:\) \(i\leq \omega \}\) with \(dist(x_ i,x_ j)=2^{-i}\) for \(i\leq j\leq \omega\), k is a cardinal, then there is a metric space Y such that k-coloring the points of Y there always exists a monocolored isometric copy of X.''