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: <@222424031368970240> `load` and `loadstring` are bad compared to... not dynamically loading/executing code. They're the best ways to do it it you have to.
gollark: Peripherals equipped on a side of a turtle block access to any external peripherals also on that side.
gollark: <@185063952093413376> Yes, though potatOS is primarily tested in emulators.
gollark: Consider making a PR.
gollark: Very exciting. Better AE2 integration could allow neat stuff.

See also

References

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


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.