Real Analysis/Limit Points (Accumulation Points)

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Definition[edit]

Let (X,d) be a metric space, and let A \subset X. We call x \in X a limit point of A if for any \epsilon > 0 there exists some y \neq x such that y \in B(x,\epsilon)\cap A.

We denote the set  lim(A) the set of all x \in X such that x is a limit point of A.