Euclidean Space is Subspace of Extended Real Number Space

Theorem
Let $\left({\overline{\R}, \tau}\right)$ be the extended real number space.

Then $\tau \restriction_{\R}$, the subspace topology on $\R$, is the Euclidean topology.

That is, Euclidean $1$-space is a Definition:Topological Subspace of the extended real number space.