\begin{definition}[Definition:Euclidean Space/Euclidean Topology/Real Number Plane]
Let $\R^n$ be an $n$-dimensional real vector space.
Let $M = \struct {\R^2, d}$ be a real Euclidean space of $2$ dimensions.
The topology $\tau_d$ induced by the Euclidean metric $d$ is called the '''Euclidean topology'''.
The space $\struct {\R^2, \tau_d}$ is known as the '''(real) Euclidean plane'''.
\end{definition}