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

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

  1. Cantor, Georg Über Unendliche, lineare punktmannigfaltigkeiten, Mathematische Annalen. 21 (1883) 545-591.


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