In topology and related areas of mathematics a **uniformly connected space** or **Cantor connected space** is a uniform space *U* such that every uniformly continuous function from *U* to a discrete uniform space is constant.

A uniform space *U* is called **uniformly disconnected** if it is not uniformly connected.

## Properties

A compact uniform space is uniformly connected if and only if it is connected

## Examples

- every connected space is uniformly connected
- the rational numbers and the irrational numbers are disconnected but uniformly connected

## See also

## References

- Cantor, Georg
*Über Unendliche, lineare punktmannigfaltigkeiten*, Mathematische Annalen. 21 (1883) 545-591.