Definition:Topological Manifold/Smooth Manifold

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Definition

Let $M$ be a second-countable locally Euclidean space of dimension $d$.

Let $\mathscr F$ be a smooth differentiable structure on $M$.


Then $\struct {M, \mathscr F}$ is called a smooth manifold of dimension $d$.


Also known as

A smooth manifold is also known as a differential manifold.


Also see

  • Results about smooth manifolds can be found here.