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 a singleton.

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

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