---
tag: J7P32JQTVE
kind: concept
name: Atlas
msc: [57N99, 58A05]
sources:
  - url: https://en.wikipedia.org/wiki/Atlas_(topology)
same_as:
  wikidata: Q1303310
  wikipedia: Atlas (topology)
---

## Summary

An atlas on a [[topological space|0CQHFPGJ45]] is a family of charts whose domains cover the space.
A chart is a homeomorphism from an open piece of the space onto an open subset of $\R^n$.
Through an atlas, questions about the space can be turned into questions about open sets of $\R^n$.
Extra structures on manifolds, such as smooth or piecewise linear structures, are defined by special atlases.
In such an atlas, the changes of chart belong to a chosen class of maps.

## Explanations

### L1 human

The word comes from a book of maps of the Earth.
Each page shows one region of the globe on a flat sheet, and the pages overlap at their edges.
No single flat page can show the whole sphere without tearing it, but a collection of pages covers everything.
For the circle, two charts suffice: one for the circle without its north pole and one for the circle without its south pole.
Where two charts overlap, a map called the transition map converts positions on one chart into positions on the other.