Uniformly connected space

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In topology and related areas of mathematics a uniformly connected space or Cantor connected space is a uniform space U so that every uniformly continuous functions from U to a discrete uniform space is constant.

A uniform space U is called uniformly disconnected if every uniformly continuous functions from a discrete uniform space to U constant.

Contents 1 Properties 2 Examples 3 See also 4 References

[edit] Properties

A compact topological space is uniformly connected if and only if it is connected

[edit] Examples

• every connected space is uniformly connected
• the rational numbers and the irrational numbers are disconnected but uniformly connected

[edit] See also

• connectedness

[edit] References

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