## Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A \subseteq S$.

### Definition from Open Neighborhood

A point $x \in S$ is an adherent point of $A$ if and only if every open neighborhood $U$ of $x$ satisfies:

$A \cap U \ne \varnothing$

### Definition from Closure

A point $x \in S$ is an adherent point of $A$ if and only if $x$ is an element of the closure of $A$.