# Open Set is G-Delta Set

## Theorem

Let $\left({X, \tau}\right)$ 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 intersection of a singleton.

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

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

$\blacksquare$