Manifold

Differentiable manifold

A 𝛼-differentiable manifold or 𝐶𝛼-manifold (𝑀,𝒜) is a topological manifold equipped with a maximal 𝐶𝛼-atlas.¹

Embedded manifolds

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

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Footnotes

1. In particular, a 𝐶0-manifold is a topological manifold with an atlas. ↩