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.
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