- Source: 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
connectedness
References
Cantor, Georg Über Unendliche, lineare punktmannigfaltigkeiten, Mathematische Annalen. 21 (1883) 545-591.
Kata Kunci Pencarian:
- Uniformly connected space
- Connected space
- Uniform space
- List of general topology topics
- Uniform property
- Metric space
- Uniformly disconnected space
- Glossary of general topology
- Hölder condition
- General topology
