Partition Topology is Zero Dimensional

Theorem
Let $T = \left({S, \tau}\right)$ be a partition space.

Then $T$ is zero dimensional.

Proof
Let $\mathcal P$ be the partition which is the basis for $T$.

From Open Set in Partition Topology is also Closed, all the elements of $\mathcal P$ are both closed and open.

Hence the result, by definition of zero dimensional space