Partition Topology is T4

Corollary to Partition Topology is T5
Let $S$ be a set and let $\PP$ be a partition on $S$ which is not the (trivial) partition of singletons.

Let $T = \struct {S, \tau}$ be the partition space whose basis is $\PP$.

Then:
 * $T$ is a $T_4$ space.

Proof
We have that the Partition Topology is $T_5$.

We also have that a $T_5$ Space is $T_4$ Space.

The result follows.