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 ![f:X->[0,1]](/images/equations/UrysohnsLemma/Inline5.svg)
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 
.
