## Differentiable manifold

An -dimensional (differentiable) manifold is a Hausdorff topological space with a countable (topological) basis, together with a maximal differentiable atlas.

This atlas consists of a family of charts where the domains of the charts, , form an open cover of , the are open in , the charts (local coordinates) are homeomorphisms, and every change of coordinates is differentiable on its domain of definition .

Source: Representations of Compact Lie Groups (Graduate Texts in Mathematics)

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