Definition:Euclidean Space/Euclidean Topology/Real Number Plane

Definition
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.

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