Let \(X\) be a topological space, \(A\subseteq X\), and \(x\in X\). The point \(x\) is a limit point of \(A\) if every neighborhood of \(x\) meets \(A\sm\ts{x}\). A limit point is also called an accumulation point.
A point \(x\in X\) is a limit point of \(A\subseteq X\) if and only if \(x\in \cl_{X}(A\sm\ts{x})\), the closure of \(A\sm\ts{x}\) in \(X\).
What is a limit point of a subset $A \subseteq X$?