Definition:Topological Manifold/Differentiable Manifold
< Definition:Topological Manifold(Redirected from Definition:Differentiable Manifold)
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Definition
Let $M$ be a second-countable locally Euclidean space of dimension $d$.
Let $\mathscr F$ be a $d$-dimensional differentiable structure on $M$ of class $\CC^k$, where $k \ge 1$.
Then $\struct {M, \mathscr F}$ is a differentiable manifold of class $\CC^k$ and dimension $d$.