Definition:Separated Sets/Definition 1

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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:

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

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


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


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