#
nLab

coordinate system

### Context

#### Manifolds and cobordisms

# Contents

## Idea

A topological manifold $X$ of dimension $n \in \mathbb{N}$ is by definition a topological space that is locally homeomorphic to a Cartesian space $\mathbb{R}^n$. A choice of such morphism

$\phi : \mathbb{R}^n \stackrel{\simeq}{\to} X|_{im(\phi)} \hookrightarrow X$

is a **coordinate system** or **coordinate chart** or just **chart** on the image of $\phi$.

This generalises to other sorts of manifolds.

An atlas is the collection of coordinate charts defining a manifold structure.

Revised on September 5, 2013 20:49:25
by

Urs Schreiber
(82.169.65.155)