Definition:Urysohn Function

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A, B \subseteq S$ such that $A \cap B = \varnothing$.

Let $f: S \to \left[{0 \,.\,.\, 1}\right]$ be a continuous mapping where $\left[{0\,.\,.\, 1}\right]$ is the unit interval.

Then $f$ is an Urysohn function for $A$ and $B$ iff:
 * $f \restriction_A = 0, f \restriction_B = 1$

that is:
 * $\forall a \in A: f \left({a}\right) = 0$
 * $\forall b \in B: f \left({b}\right) = 1$