Definition:Omega-Accumulation Point
Jump to navigation
Jump to search
Definition
Let $T = \struct {S, \tau}$ 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
- Definition:Omega-Limit Point
- Results about $\omega$-accumulation 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