Partition Topology is T3 1/2

Theorem
Let $S$ be a set and let $\mathcal P$ be a partition on $S$.

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

Then $T$ is a $T_{3 \frac 1 2}$ space.

Thus $T$ is also a $T_3$ space.