Sub-Basis for Real Number Line

Theorem
Let the real number line $$\R$$ be considered as a topology under the usual metric.

Then $$\left\{{\left({\infty \, . \, . \, a}\right),\left({b \, . \, . \, \infty}\right): a, b \in \R}\right\}$$ is a sub-basis for $$\R$$.