Definition:Dimension (Topology)/Locally Euclidean Space

Definition
Let $M$ be a locally Euclidean space.

Let $\left( { U, \kappa } \right)$ be a coordinate chart such that:
 * $\displaystyle \kappa : U \to \kappa \left( {U} \right) \subseteq \R^n $

Then the natural number $n \ge 0$ is called the dimension of the locally Euclidean space.

Also See
Definition:Dimension (Linear Algebra)

Definition:Topological Manifold