Definition:Adherent Point/Definition 3

Definition

Let $T = \struct{S, \tau}$ be a topological space.

Let $H \subseteq S$.

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

$H \cap N \ne \O$

Also see

• Definition:Condensation Point
• Definition:Limit Point of Set
• Definition:Omega-Accumulation Point

• Relationship between Limit Point Types

• Results about adherent points can be found here.

Sources

• 1971: William W. Fairchild and Cassius Ionescu Tulcea: Topology: $3$: Interior of a Set and Adherence of a Set, Definition $3.9$