===== Atlas =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $\langle M,T\rangle$ ... second-countable Hausdorff space |
| @#55CCEE: context     | @#55CCEE: $n\in \mathbb N$ |
| @#FFBB00: definiendum | @#FFBB00: $A\in$ it |
| @#AAFFAA: inclusion   | @#AAFFAA: $A\subseteq$ chart $\left(\langle M,T\rangle,n\right)$ |
| @#FFFDDD: forall      | @#FFFDDD: $x\in M$ |
| @#FFFDDD: exists      | @#FFFDDD: $\langle U,\varphi\rangle\in A$ |
| @#55EE55: postulate   | @#55EE55: $x\in U$ |

==== Discussion ====
=== Idea ===
An atlas is a set of [[chart|charts]], so that no point $x\in M$ is left out from being mapped to $\mathbb R^n$.

=== Alternative definitions ===
One can equivalently postulate that $M$ is covered by the union of all the open subsets $U$ given with the charts $\langle U,\varphi\rangle$ of an atlas $A$:

$\bigcup_{chart\in A}\pi_1(chart)=M$.

=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Atlas_%28topology%29|Atlas (topology)]]
==== Parents ====
=== Context* ===
[[Second-countable Hausdorff space]], [[Natural number]]
=== Subset of ===
[[Chart]]