# 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 $d$**.

## Also see

## Sources

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