# Closed Subset of Real Number Space is G-Delta

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## Theorem

Let $\left({\R, \tau_d}\right)$ be the real number line considered as a topological space under the usual (Euclidean) topology.

Let $H \subseteq \R$ be a closed subset of $\R$.

Then $H$ is a $G_\delta$ set.

## Proof

We have:

Real Number Line is Metric Space
Closed Set in Metric Space is $G_\delta$

Hence the result.

$\blacksquare$