Definition:Omega-Accumulation Point

Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A \subseteq S$.

An $\omega$-accumulation point of $A$ is a limit point $x$ of $A$ such that every open set containing $x$ also contains an infinite number of points of $A$.

Also see

• Definition:Condensation Point
• Definition:Limit Point of Set
• Definition:Adherent Point
• Definition:Accumulation Point

• Relationship between Limit Point Types

• Results about $\omega$-accumulation points can be found here.

Sources

• 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology ... (previous) ... (next): $\text{I}: \ \S 1$: Limit Points