\begin{definition}[Definition:Separated Sets/Definition 2]
Let $T = \struct {S, \tau}$ be a topological space.
Let $A, B \subseteq S$.
$A$ and $B$ are '''separated (in $T$)''' {{iff}} 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 $T$)'''.
Category:Definitions/Topology
\end{definition}