Real Number Line is First-Countable

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

Then $\left({\R, \tau_d}\right)$ is first-countable.

Proof
From Real Number Space is Second-Countable we have that $\left({\R, \tau_d}\right)$ is a second-countable space.

The result follows from Second-Countable Space is First-Countable.