Definition:Separated Points

Definition
Let $\left({S, \tau}\right)$ 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.