Definition:Adherent Point

Definition
Let $T = \left({X, \tau}\right)$ 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 neighborhood $U$ 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


 * Condensation Point
 * $\omega$-Accumulation Point
 * Limit Point


 * Relationship between Limit Point Types