Partition of Singletons yields Discrete Topology

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Let $S$ be a set which is non-empty.

Let $\PP$ be the (trivial) partition of singletons on $S$:

$\PP = \set {\set x: x \in S}$

Then the partition topology on $\PP$ is the discrete topology.


From Basis for Discrete Topology it is shown that $\PP$ as defined here forms the basis of the discrete topology.