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.

A uniform space U is called uniformly disconnected if it is not uniformly connected.

Properties[edit]

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

Examples[edit]

See also[edit]

References[edit]

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