In
mathematics, a
completely metrizable space (
metrically 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. The term
topologically complete space is employed by some authors as a synonym for
completely metrizable space, but sometimes also used for other classes of topological spaces, like
completely uniformizable spaces or Cech-complete spaces.