# Examples

### Because it’s always better with examples

### Big classes of examples

Most commonly encountered topological spaces are paracompact, which makes it a pervasive notion.

- Obviously every compact topological space is paracompact;
- All metric spaces are paracompact;
- All regular Lindelöf spaces are paracompact. In particular, all CW complexes are paracompact;

### One dimentional complex manifolds

Suppose we have a Hausdorff topological space with a holomorphic and one
dimentional atlas, then surprisingly, it *has to be* paracompact [1]. Hence,
there is no complex analogue of the long
line.

Such a property is very specific to complex dimension one.

## References

- [1] Ahlfors & Sario,
*Riemann surfaces*