# 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

*connectedness

References

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

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