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 is inevitable.
gollark: Edge is basically just Chromium now anywya.
gollark: They like backward compatibility so obviously there'll just be some sort of extreme WINE thing.
gollark: See, MS likely doesn't want to maintain their own kernel and stuff. The implications are obviously obvious: MS is looking to port Windows to run on the Linux kernel, and thingying Edge is a test.
gollark: Or a test for the confusing future of Windows for Linux™.

See also

References

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


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