Open Set is G-Delta Set

Theorem
Let $$\left({X, \vartheta}\right)$$ be a topological space.

Let $$U$$ be an open set of $$X$$.

Then $$U$$ is a $G_\delta$ set of $$X$$.

Proof
$$U$$ is the union of one set.

So $$U$$ is trivially the union of a countable number of open sets of $$X$$.

The result follows by definition of $G_\delta$ set.