Euclidean Space is Subspace of Extended Real Number Space

Theorem

Let $\struct {\overline \R, \tau}$ 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 subspace of the extended real number space.

Proof

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