Open Set in Partition Topology is Component

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

Then each of its open sets are components of $T$.

Proof
Let the partition $\mathcal P$ be a basis of $T$.

From Open Sets in Partition Topology also Closed, open sets are in fact clopen.

So the elements of $\mathcal P$ are clopen.

The result follows from the definition of components.