Manifold

Differentiable manifold

A -differentiable manifold or -manifold is a topological manifold equipped with a maximal -atlas.1

note

If that’s confusing, the canonical example is Real coördinate space

Embedded manifolds

By the Whitney embedding theorem, we may alternatively consider -manifolds as embedded into real coördinate space, i.e. as a Real embedded manifold.

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Footnotes

  1. In particular, a -manifold is a topological manifold with an atlas. ↩