Euclidean Space is Subspace of Extended Real Number Space
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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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