Definition:Separated Sets/Definition 2
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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 there exist $U,V\in\tau$ with:
- $A \subset U$ and $U \cap B = \O$
- $B \subset V$ and $V \cap A = \O$
where $\O$ denotes the empty set.
$A$ and $B$ are said to be separated sets (of $T$).