In mathematics, a completely metrizable space (complete topological space or topologically complete space) is a topological space (X, T) for which there exists at least one metric d on X such that (X, d) is a complete metric space and d induces the topology T. This is equivalent to the condition that X is metrizable and a Gδ in its Stone–Čech compactification βX.
The set of rational numbers is an example of a topological space that is metrizable but not completely metrizable.
Famous quotes containing the words space and/or completely:
“... the movie woman’s world is designed to remind us that a woman may live in a mansion, an apartment, or a yurt, but it’s all the same thing because what she really lives in is the body of a woman, and that body is allowed to occupy space only according to the dictates of polite society.”
—Jeanine Basinger (b. 1936)
“I also believe that few people remain completely untouched by the thought that instead of the life they lead there might also be another, where all actions proceed from a very personal state of excitement. Where actions have meanings, not just causes. And where a person, to use a trivial word, is happy, and not just nervously tormenting himself.”
—Robert Musil (1880–1942)