Adherent point
In mathematics, an adherent point (also closure point or point of closure or contact point) of a subset A {\displaystyle A} of a topological space X , {\displaystyle X,} is a point x {\displaystyle x} in X {\displaystyle X} such that every neighbourhood of x {\displaystyle x} (or equivalently, every open neighborhood of x {\displaystyle x} ) contains at least one point of A . {\displaystyle A.} A point x ∈ X {\displaystyle x\in X} is an adherent point for A {\displaystyle A} if and only if x {\displaystyle x} is in the closure of A , {\displaystyle A,} thus x ∈ Cl X A {\displaystyle x\in \operatorname {Cl} _{X}A} if and only if for all open subsets U ⊆ X , {\displaystyle U\subseteq X,} if x ∈ U then U ∩ A ≠ ∅ .