Complete uniform space
A uniform space in which every Cauchy filter converges. An important example is a complete metric space. A closed subspace of a complete uniform space is complete; a complete subspace of a separable uniform space is closed. The product of complete uniform spaces is complete; conversely, if the product of non-empty uniform spaces is complete, then all the spaces are complete. Any uniform space can be uniformly and continuously mapped onto some dense subspace of a complete uniform space (see Completion of a uniform space).
|||N. Bourbaki, "Elements of mathematics. General topology" , Addison-Wesley (1966) (Translated from French)|
|||J.L. Kelley, "General topology" , Springer (1975)|
|[a1]||J.R. Isbell, "Uniform spaces" , Amer. Math. Soc. (1964)|
Complete uniform space. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Complete_uniform_space&oldid=14972