In mathematics, a completely metrizable space[1] (metrically topologically complete space[2]) 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,[3] but sometimes also used for other classes of topological spaces, like completely uniformizable spaces[4] or Čech-complete spaces.