Sub_Basis_for_Real_Number_Line

Let the real number line $\R$ be considered as a topology under the usual (Euclidean) metric. Then $\mathcal B := \left\{{\left({-\infty \,.\,.\, a}\right), \left({b \,.\,.\, \infty}\right): a, b \in \R}\right\}$ is a sub-basis for $\R$.