limit point
noun1
Mathematics, Sciences, Topology Given a subset S of a given topological space T, any point p whose every neighborhood contains some point, distinct from p, which belongs to S.
- is an example of a function having infinitely many essential singularities with a limit point at z=0. It is an easy matter to give examples of "elementary" functions whose singularities have a countable number of limit points.1962 [Ginn and Company], Einar Hille, Analytic Function Theory, Volume 2, 2005, American Mathematical Society, page 19, The function sin ( cot 1/z)
- If z_0 is a limit point of S, then every ϵ-neighborhood of z_0 must contain infinitely many points of S.1970 [Macmillan], John W. Dettman, Applied Complex Variables, 1984, Dover, unnumbered page, Let S' be the set of limit points of a set S. Then the closure ◌̅S of S is S∪S'. […]
1 more example
- As the next example shows, the set of zeros may well have a limit point not belonging to the domain.2006, Ivan Francis Wilde, Lecture Notes on Complex Analysis, Imperial College Press, page 153:
- Synonyms
- accumulation point, cluster point
- Related terms
- limit