Definition:Euclidean Space/Euclidean Topology/Real Number Line

Definition
Let $\R$ be the set of real numbers.

Let $M = \left({\R, d}\right)$ be the real number line under the Euclidean metric $d$.

The topology $\tau_d$ induced by $d$ is called the Euclidean topology.

Also known as
The Euclidean topology is sometimes called the usual topology.