Definition:Topological Manifold/Smooth Manifold

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

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

Then $\left({M, \mathscr F}\right)$ is called a smooth manifold of dimension $d$.

Also see

 * Differentiable Manifold