nLab
coordinate system

Contents

Idea

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

ϕ: nX| im(ϕ)X \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 ϕ\phi.

This generalises to other sorts of manifolds.

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

Revised on January 14, 2015 21:23:50 by Urs Schreiber (82.113.98.172)