Complete topological space
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Complete topological space may refer to:
- a topological space equipped with an additional Cauchy space structure which is complete,
- e. g., that it is a complete uniform space with respect to an aforementioned uniformity,
- e. g., that it is a complete metric space with respect to an aforementioned metric;
- e. g., that it is a complete uniform space with respect to an aforementioned uniformity,
- a topological space with 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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