Definition:Dimension (Topology)

Definition

Locally Euclidean Space

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 $M$.