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.
展开▼
机译：我们证明了解析集的一个分区定理，即，如果X是波兰空间中的一个解析集，并且[X] n = K0 K1且K0在相对拓扑中开放，并且该分区满足最终条件，那么要么存在一个完美的K0均匀子集或X是K1均匀子集的可数并集。我们还证明了三维情况下解析集的一个分区定理。最后，我们给出定理的一些应用。
展开▼
