Topological atlas
= Topological atlas
{title2=$\mathcal A$}
A topological atlas is a family $\mathcal A=\{(U_i,\varphi_i)\}$ of <coordinate charts> whose domains form an <open cover> of a <topological manifold>. Each point must belong to at least one chart domain; no individual domain needs to cover the entire <topological manifold>. On overlaps, <topological transition maps> describe the same points in two coordinate systems.