Quotient Topology of Partition Topology is Discrete Space

Theorem
Let $\mathcal P$ be a partition of a set $S$.

Let $T = \left({S, \vartheta}\right)$ be the partition space formed from $\mathcal P$.

Let $S / \mathcal P$ be the quotient set of $S$ by $\mathcal P$.

Then the quotient topology $\vartheta_{S / \mathcal P}$ is a discrete topology.