= Partition topology
Given a partition of a <set>, declare a subset open precisely when it is a union of partition blocks. Arbitrary unions and finite intersections of such unions are again unions of blocks, giving a <topology>. The quotient map to the block set with its <discrete topology> pulls that topology back to the original set. For the partition of $\mathbb Z$ into its two parity classes, the only open sets are the empty set, those two classes, and all of $\mathbb Z$.
Back to article page
