Uniformly connected space
(Redirected from Uniformly disconnected)
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
[edit]A compact uniform space is uniformly connected if and only if it is connected.
Examples
[edit]- Every connected space is uniformly connected.
- The rational numbers and the irrational numbers are disconnected but uniformly connected.
See also
[edit]References
[edit]- Cantor, Georg Über Unendliche, lineare punktmannigfaltigkeiten, Mathematische Annalen. 21 (1883) 545-591.
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