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Uniformly connected space

From Wikipedia, the free encyclopedia
Type of uniform space

Intopology and related areas ofmathematics auniformly connected space orCantor connected space is auniform spaceU such that everyuniformly continuous function fromU to adiscrete uniform space is constant.

Auniform spaceU is calleduniformly disconnected if it is not uniformly connected.

Properties

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Acompactuniform space is uniformly connectedif and only if it isconnected.

Examples

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See also

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References

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


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