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
gollark: It's weird how no other consumer standards are optical.
gollark: "Optical audio" is TOSLINK, which is actually digital.
gollark: I find it kind of triangular myself.
gollark: Why send stuff wirelessly using a solar panel or whatever when you could just connect the speaker to the mobile network and email music to it?
gollark: Is this using a magnetron or something? A flamethrower is probably still more powerful.
See also
References
- Cantor, Georg Über Unendliche, lineare punktmannigfaltigkeiten, Mathematische Annalen. 21 (1883) 545-591.
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