Atlases

Let be a topological space. A chart on consists of an open subset of , and a homeomorphism from to an open subset of some Euclidean space . Somewhat informally, one may refer to a chart , meaning that the image of is an open subset of , and that is a homeomorphism onto its image; in the usage of some authors, this may instead mean that is itself a homeomorphism.

The presence of a

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