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

Also known as

A smooth manifold is also known as a differential manifold.

A smooth manifold of dimension $d$ is also known as a smooth $d$-manifold.

Also see

• Differentiable Manifold

• Results about smooth manifolds can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): manifold
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): smoothing
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): manifold
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): smoothing