# Complete topological space

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

- that has been 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,
- or that has some topological property related to the above:
- that it is completely metrizable (often called
*(metrically) topologically complete*), - or that it is completely uniformizable (also called
*topologically complete*by some authors).

- that it is completely metrizable (often called