Definition:Separated Sets/Definition 2

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

Let $A, B \subseteq S$.

$A$ and $B$ are separated (in $T$) there exist $U,V\in\tau$ with:
 * $A \subset U$ and $U \cap B = \O$
 * $B \subset V$ and $V \cap A = \O$

where $\O$ denotes the empty set.

$A$ and $B$ are said to be separated sets (of $T$).