  We investigate the existence of metric spaces which, for any coloring with a
fixed number of colors, contain monochromatic isomorphic copies of a fixed
starting space K. In the main theorem we construct such a space of size
\(2^{\aleph_0}\) for colorings with \(\aleph_0\) colors and any metric space
\(K\) of size \(\aleph_0\). We also give a slightly weaker theorem for
countable ultrametric \(K\) where, however, the resulting space has
size~\(\aleph_1\).
