Atlas

Summary

An atlas on a topological space 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.