Partition Topology is Zero Dimensional

Theorem

Let $T = \struct {S, \tau}$ be a partition space.

Then $T$ is zero dimensional.

Proof

Let $\PP$ be the partition which is the basis for $T$.

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

Hence the result, by definition of zero dimensional space

$\blacksquare$