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

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): dimension: 4. (of a manifold)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dimension: 4. (of a manifold)
• 2003: John M. Lee: Introduction to Smooth Manifolds: $\S 1$: Topological Manifolds