# Definition:Separated Sets/Definition 1

## Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $A, B \subseteq S$.

$A$ and $B$ are separated (in $T$) if and only if:

$A^- \cap B = A \cap B^- = \O$

where:

$A^-$ denotes the closure of $A$ in $T$
$\O$ denotes the empty set.

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