\begin{definition}[Definition:Separated by Neighborhoods/Sets/Open Sets]
Let $T = \struct {S, \tau}$ be a topological space.
Let $A, B \subseteq S$ such that:
:$\exists U, V \in \tau: A \subseteq U, B \subseteq V: U \cap V = \O$
That is, that $A$ and $B$ both have open neighborhoods in $T$ which are disjoint.
Then $A$ and $B$ are described as '''separated by (open) neighborhoods'''.
Category:Definitions/Separated by Neighborhoods
\end{definition}