We prove that, for every n, the topological space { \omega}_n^{ \omega} (where { \omega}_n has the discrete topology) can be partitioned into { \omega}_n copies of the Baire space. Using this fact, the authors then prove two new theorems about completely ultrametrizable spaces. We say that Y is a condensation of X if there is a continuous bijection from X to Y. First, it is proved that the Baire space is a condensation of { \omega}_n^{ \omega} if and only if it can be partitioned into { \omega}_n Borel sets, and some consistency results are given regarding such partitions. It is also proved that it is consistent with ZFC that, for any n < { \omega}, the continuum is { \omega}_n and there are exactly n+3 similarity types of perfect completely ultrametrizable spaces of size continuum. These results answer two questions of the first author from a previous paper.
Categories: math.GN