Definition:Dimension (Topology)

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 $\struct {U, \kappa}$ 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 $M$.