Coordinate Maps
The concept of a coordinate map, or 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 Rn. 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 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.
Read more about this topic: Coordinate System
Famous quotes containing the word maps:
“And at least you know
That maps are of time, not place, so far as the army
Happens to be concernedthe reason being,
Is one which need not delay us.”
—Henry Reed (19141986)