Definition:Condensation Point

Definition

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

Let $A \subseteq X$.

A condensation point of $A$ is a limit point $x$ of $A$ such that every open set containing $x$ also contains an uncountable number of points of $A$.

Also see

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

• Relationship between Limit Point Types

• Results about condensation 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