Definition:Dimension (Topology)/Locally Euclidean Space

Definition

Let $M$ be a locally Euclidean space of dimension $n$.

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

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)
• 2011: John M. Lee: Introduction to Topological Manifolds (2nd ed.): Chapter $1$: Topological Spaces : $\S$: Manifolds
• 2013: John M. Lee: Introduction to Smooth Manifolds (2nd ed.): $\S 1$: Topological Manifolds