Atlas

Set

context $\langle M,T\rangle$ … second-countable Hausdorff space
context $n\in \mathbb N$
definiendum $A\in$ it
inclusion $A\subseteq$ chart $\left(\langle M,T\rangle,n\right)$
forall $x\in M$
exists $\langle U,\varphi\rangle\in A$
postulate $x\in U$

Discussion

Idea

An atlas is a set of 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: Atlas (topology)

Parents

Context*

Subset of

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