Supriya Ghosh (Editor)

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 such that every uniformly continuous function from U to a discrete uniform space is constant.

Contents

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

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

    Uniformly connected space Wikipedia


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