Definition:Separated Sets/Definition 2

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Definition

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

Let $A, B \subseteq S$.


$A$ and $B$ are separated (in $T$) if and only if there exist $U,V\in\tau$ with:

$A\subset U$ and $U\cap B = \varnothing$
$B\subset V$ and $V\cap A = \varnothing$

where $\varnothing$ denotes the empty set.


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