# Urysohn lemma

From Conservapedia

The **Urysohn lemma** states:

If

A,Bare two disjoint, closed subsets of a normal spaceX, then there exist a continuous functionf:X→ [0, 1], such thatf(A)= 0 andf(B)= 1.

The converse of the Urysohn lemma also holds: if there is such a continuous function for any two disjoint closed sets *A* and *B* in *X*, then *X* is normal.