Definition:Adherent Point

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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 $A$.


Also see

  • Results about adherent points can be found here.