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 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.
This article is issued from Wikipedia - version of the 12/1/2012. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.