Definition:Separated by Neighborhoods/Sets/Neighborhoods

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $A, B \subseteq S$ such that:
 * $\exists N_A, N_B \subseteq S: \exists U, V \in \tau: A \subseteq U \subseteq N_A, B \subseteq V \subseteq N_B: N_A \cap N_B = \O$

That is, that $A$ and $B$ both have neighborhoods in $T$ which are disjoint.

Then $A$ and $B$ are described as separated by neighborhoods.