For any metric space "M", one can construct a complete metric space "M′" (which is also denoted as ), which contains "M" as a dense subspace. It has the following universal property: if "N" is any complete metric space and "f" is any uniformly continuous function from "M" to "N", then there exists a unique uniformly continuous function "f′" from "M′" to "N" that extends "f". The space "M"' is determined up to isometry by this property (among all complete metric spaces isometrically containing "M"), and is called the "completion" of "M".