Let ( X , d ) {\displaystyle (X,d)} be a metric space, and let A ⊂ X {\displaystyle A\subset X} . We call x ∈ X {\displaystyle x\in X} a limit point of A {\displaystyle A} if for any ϵ > 0 {\displaystyle \epsilon >0} there exists some y ≠ x {\displaystyle y\neq x} such that y ∈ B ( x , ϵ ) ∩ A {\displaystyle y\in B(x,\epsilon )\cap A} .
We denote the set l i m ( A ) {\displaystyle lim(A)} the set of all x ∈ X {\displaystyle x\in X} such that x {\displaystyle x} is a limit point of A {\displaystyle A} .
