In mathematics, a topological space (X, T) is called completely uniformizable[1] (or Dieudonné complete[2]) if there exists at least one complete uniformity that induces the topology T. Some authors[3] additionally require X to be Hausdorff.
Some authors have called these spaces topologically complete,[4] although that term has also been used in other meanings like completely metrizable, which is a stronger property than completely uniformizable.
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.
This topology-related article is a stub.