\begin{definition}[Definition:Euclidean Space/Euclidean Topology/Real]
Let $\R^n$ be an $n$-dimensional real vector space.
Let $M = \struct {\R^n, d}$ be a real Euclidean $n$-space.
The topology $\tau_d$ induced by the Euclidean metric $d$ is called the '''Euclidean topology'''.
\end{definition}