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: If it is right, why is it wrong? Explain that.
gollark: Wrong.
gollark: No you don't.
gollark: Maybe it likes weird NOPs.
gollark: It's "unlimited unless you start using more than we expect a regular person would".

See also

References

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


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