Definition:Separated Sets

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A, B \subseteq S$.

Then $A$ and $B$ are separated (in $T$) :
 * $A^- \cap B = A \cap B^- = \varnothing$

where $A^-$ denotes the closure of $A$ in $T$, and $\varnothing$ denotes the empty set.

$A$ and $B$ are said to be separated sets (of $T$).

Also known as
When $A$ and $B$ are separated in $T$, they are said to separate $T$.