Singleton Partition yields Indiscrete Topology

Theorem
Let $S$ be a set which is not empty.

Let $\mathcal P$ be the (trivial) singleton partition $\left\{{S}\right\}$ on $S$.

Then the partition topology on $\mathcal P$ is the indiscrete topology.

Proof
By definition, the partition topology on $\mathcal P$ is the set of all unions from $\mathcal P$.

This is (trivially, and from Union of Empty Set) $\left\{{\varnothing, S}\right\}$ which is the indiscrete topology on $S$ by definition.