Definition:Dimension (Topology)/Locally Euclidean Space
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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
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