# Uniformly connected space

- Uniformly connected space
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 functions from "U" to a discrete uniform space is constant.

A uniform space "U" is called **uniformly disconnected** if every uniformly continuous functions from a discrete uniform space to "U" is constant.

** 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 **

*connectedness

** References **

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

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