Definition:Adherent Point/Definition 2

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 $x$ is an element of the closure of $H$.

Also see

• Equivalence of Definitions of Adherent Point

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

• Relationship between Limit Point Types

• Results about adherent points can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): adherent point (Topology)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): adherent point