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:
 * $\kappa: U \to \kappa \left({U}\right) \subseteq \R^n$

for some $n \in \N$.

Then the natural number $n$ is called the dimension of $M$.

Also see
Definition:Dimension (Linear Algebra)

Definition:Topological Manifold