\begin{definition}[Definition:Euclidean Space/Euclidean Topology]
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'''.
\end{definition}