Definition:Topological Manifold/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 $\mathcal C^k$, where $k \ge 1$.


Then $\left({M, \mathscr F}\right)$ is a differentiable manifold of class $C^k$ and dimension $d$.


Also see