Definition:Euclidean Space/Euclidean Topology/Real

Definition
Let $\R^n$ be an $n$-dimensional real vector space.

Let $M = \left({\R^n, d}\right)$ be a real Euclidean $n$-space.

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

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