Meanings
plural limit points
- mathematicsGiven 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 1532 more examples
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'. […]Synonyms: accumulation point, cluster point
Synonyms & antonyms
nounGiven 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.
More synonyms by meaning
nounthe mathematical value toward which a function goes as the independent variable approaches infinity
Synonym sets from Open English WordNet, CC BY 4.0.
Translations
Dutch verdichtingspunt
- verdichtingspuntpoint whose every neighborhood contains a point in a given subset
Finnish rajapiste
- rajapistepoint whose every neighborhood contains a point in a given subset
French point d'accumulation
- point d'accumulationpoint whose every neighborhood contains a point in a given subset
German Häufungspunkt
- Häufungspunktpoint whose every neighborhood contains a point in a given subset
Hebrew נקודת גבול
- נקודת גבול (nekudát gvúl)point whose every neighborhood contains a point in a given subset
Italian punto di accumulazione
- punto di accumulazionepoint whose every neighborhood contains a point in a given subset
Polish punkt skupienia
- punkt skupieniapoint whose every neighborhood contains a point in a given subset
Cite this entry
limit point. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/limit%20point
“limit point.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/limit%20point. Accessed November 3, 2026.
WatkinsX Dictionary, s.v. “limit point,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/limit%20point.
Source: limit point on Wiktionary, CC BY-SA 4.0.