Definition:Euclidean Space/Euclidean Topology

Definition
Let $S$ be one of the standard number fields $\Q$, $\R$, $\C$.

Let $S^n$ be a cartesian space for $n \in \N_{\ge 1}$.

Let $M = \struct {S^n, d}$ be a Euclidean space.

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

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