\begin{definition}[Definition:Separation (Topology)]
Let $T = \struct {S, \tau}$ be a topological space.
Let $A$ and $B$ be open sets of $T$.
$A$ and $B$ form a '''separation of $T$''' {{iff}}:
:$(1): \quad A$ and $B$ are non-empty
:$(2): \quad A \cup B = S$
:$(3): \quad A \cap B = \O$
That is, {{iff}} $A$ and $B$ form a partition of the set $S$.
Such a '''separation''' can be denoted:
:$A \mid B$
$A$ and $B$ are said to '''separate $T$'''.
\end{definition}