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Uniformly Connected Space

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.A compact uniform space is uniformly connected if and only if it is connected.