Abstract

We prove a partition theorem for analytic sets, namely, if X is an analytic set in a Polish space and [X]n = K0 ∪ K1 with K0 open in the relative topology, and the partition satisfies a finitary condition, then either there is a perfect K0-homogeneous subset or X is a countable union of K1-homogeneous subsets. We also prove a partition theorem for analytic sets in the three-dimensional case. Finally, we give some applications of the theorems