Dictionary

limit point en · NOUN

Meanings

1. 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.
   • 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:
   • 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'. […]

Forms

Relateds

limit

Synonyms

cluster point (point whose every neighborhood contains a point in a given subset) · accumulation point (point whose every neighborhood contains a point in a given subset)

Translations (7)

nl verdichtingspunt (point whose every neighborhood contains a point in a given subset) · fi rajapiste (point whose every neighborhood contains a point in a given subset) · fr point d'accumulation (point whose every neighborhood contains a point in a given subset) · de Häufungspunkt (point whose every neighborhood contains a point in a given subset) · pl punkt skupienia (point whose every neighborhood contains a point in a given subset) · it punto di accumulazione (point whose every neighborhood contains a point in a given subset) · he נקודת גבול (point whose every neighborhood contains a point in a given subset)