Complete topological space

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In mathematics, if a topological space X is said to be complete, it may mean:

  • that X has been equipped with an additional Cauchy space structure which is complete,
  • or that X has some topological property related to the above:
    • that it is completely metrizable (often called (metrically) topologically complete),
    • or that it is Čech-complete (a property coinciding with completely metrizability on the class of metrizable spaces, but including some non-metrizable spaces as well),
    • or that it is completely uniformizable (also called topologically complete or Dieudonné-complete by some authors).

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