A characterization of normal spaces which states that a topological space is normal iff, for any two nonempty closed disjoint subsets , and of , there is a continuous map such that and . A function with this property is called a Urysohn function.
This formulation refers to the definition of normal space given by Kelley (1955, p. 112) or Willard (1970, p. 99). In the statement for an alternative definition (e.g., Cullen 1968, p. 118), the word "normal" has to be replaced by .