Definition:Adherent Point

Definition
Let $$X$$ be a topological space.

Let $$A \subseteq X$$.

Definition by Open Neighborhood
A point $$x \in X$$ is called an adherent point of $$A$$ if every open set $$U$$ of $$x$$ satisfies $$A \cap U \ne \varnothing$$.

Definition from Closure
Equivalently, $$x$$ is an adherent point of $$A$$ if $$x$$ belongs to the closure of $$A$$.

Also see

 * Equivalence of Adherent Point Definitions


 * Limit point