Definition:Separation (Topology)

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

Then a partition $$A | B$$ of $$T$$ is a pair of subspaces $$A, B \subseteq T$$ such that:
 * $$A$$ and $$B$$ form a (set) partition of the set $$S$$;
 * Both $$A$$ and $$B$$ are open in $$T$$.

It follows that not only are $$A$$ and $$B$$ are open in $$T$$, they are also both (by definition) closed in $$T$$.