[[Manifold]]
# Differentiable manifold

A $\alpha$-**differentiable manifold** or $C^\alpha$-manifold $(M, \mathscr{A})$ is a [[topological manifold]] equipped with a maximal $C^\alpha$-[[atlas]].[^1]

## Embedded manifolds

By the [[Whitney embedding theorem]], we may alternatively consider $C^\infty$-manifolds as embedded into [[real coördinate space]], i.e. as a [[Real embedded manifold]].

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[^1]: In particular, a $C^0$-manifold is a [[topological manifold]] with an atlas.