Definition:Dimension (Topology)
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This page is about Dimension in the context of topology. For other uses, see Dimension.
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 $M$.
Hausdorff Dimension
Definition:Dimension (Topology)/Hausdorff Dimension
Lebesgue Covering Dimension
Definition:Dimension (Topology)/Lebesgue Covering Dimension