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Uniformly connected space
In topology and related areas of mathematics a uniformly connected space or Cantor connected space is a uniform space U so that every uniformly continuous functions from U to a discrete uniform space is constant.
A uniform space U is called uniformly disconnected if every every uniformly continuous functions from a discrete uniform space to U constant.
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Properties
A compact topological 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.
12-03-2008 10:22:39
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details