# Category:Manifolds

This category contains results about Manifolds in the context of Topology.

Definitions specific to this category can be found in Definitions/Manifolds.

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

Then $M$ is a **topolofical manifold of dimension $d$**.

### Differentiable Manifold

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 $d$**.

### Smooth Manifold

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 $d$**.

### Complex Manifold

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

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

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

## Subcategories

This category has the following 4 subcategories, out of 4 total.

### D

### S

## Pages in category "Manifolds"

The following 21 pages are in this category, out of 21 total.