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In mathematics, the partition topology is a topology that can be induced on any set X by partitioning X into disjoint subsets P; these subsets form the basis for the topology. There are two important examples which have their own names:
The trivial partitions yield the discrete topology or indiscrete topology.
Any set X with a partition topology generated by a partition P can be viewed as a pseudometric space with a pseudometric given by:
This is not a metric unless P yields the discrete topology.
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