Definition:Dimension (Topology)/Locally Euclidean Space

Definition
Let $M$ be a locally Euclidean space.

Let $\struct {U, \kappa}$ be a coordinate chart such that:
 * $\kappa: U \to \map \kappa U \subseteq \R^n$

for some $n \in \N$.

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

Also see

 * Dimension of Locally Euclidean Space is Well-Defined
 * Definition:Topological Manifold