Definition:Adherent Point/Definition 1

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 open neighborhood $U$ of $x$ satisfies:

$H \cap U \ne \O$

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

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Limit Points