Closure ($\overline{A}$)

The closure of a subset is the smallest closed set containing it, equivalently the set of points whose every neighbourhood meets it.

An adherent point of $A$ is a point whose every neighbourhood meets $A$. The set of adherent points is the closure of $A$. This includes all points of $A$, even isolated ones; a limit point in the accumulation-point convention instead requires each neighbourhood to meet $A\setminus \{x\}$.