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 into its two parity classes, the only open sets are the empty set, those two classes, and all of .
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Partition topology is a concept used in the field of topology, specifically in the study of different ways to define topological structures on a set. It involves creating a topology by considering a partition of a set. ### Definitions: - **Set**: A collection of distinct objects, considered as an object in its own right.