Editing Coordinate system (section)

==Coordinate maps==
{{Main|Coordinate map}}
{{Further|Manifold}}
The concept of a ''coordinate map'', or ''coordinate chart'' is central to the theory of manifolds. A coordinate map is essentially a coordinate system for a subset of a given space with the property that each point has exactly one set of coordinates. More precisely, a coordinate map is a [[homeomorphism]] from an open subset of a space ''X'' to an open subset of '''R'''<sup>''n''</sup>.<ref>Munkres, James R. (2000) ''Topology''. Prentice Hall. {{ISBN|0-13-181629-2}}.</ref> It is often not possible to provide one consistent coordinate system for an entire space. In this case, a collection of coordinate maps are put together to form an [[atlas (topology)|atlas]] covering the space. A space equipped with such an atlas is called a ''manifold'' and additional structure can be defined on a manifold if the structure is consistent where the coordinate maps overlap. For example, a [[differentiable manifold]] is a manifold where the change of coordinates from one coordinate map to another is always a differentiable function.