Definition:Omega-Accumulation Point

Definition

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

Let $A \subseteq X$.

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

• Condensation Point
• Limit Point
• Adherent Point

• Relationship between Limit Point Types

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

Sources

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