\begin{definition}[Definition:Separated Points]
Let $\struct {S, \tau}$ be a topological space.
Let $x, y \in S$ such that both of the following hold:
:$\exists U \in \tau: x \in U, y \notin U$
:$\exists V \in \tau: y \in V, x \notin V$
Then $x$ and $y$ are '''separated points'''.
\end{definition}