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Completely uniformizable space

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Completely uniformizable space

In mathematics, a topological space (X, T) is called completely uniformizable[1] (or Dieudonné complete[2] or topologically complete[3]) if there exists at least one complete uniformity that induces the topology T. Some authors additionally require X to be Hausdorff. The term topologically complete is also often used for complete metrizability, which is a stronger condition than complete uniformizability.

Properties

Every metrizable space is paracompact, hence completely uniformizable. As there exist metrizable spaces that are not completely metrizable, complete uniformizability is a strictly weaker condition than complete metrizability.

See also

Notes

References

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