See limit point in All languages combined, or Wiktionary
Download JSON data for limit point meaning in English (3.4kB)
{
"forms": [
{
"form": "limit points",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "limit point (plural limit points)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Topology",
"orig": "en:Topology",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"ref": "1962 [Ginn and Company], Einar Hille, Analytic Function Theory, Volume 2, 2005, American Mathematical Society, page 19, The function sin ( cot 1/z)",
"text": "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."
},
{
"ref": "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'. […]",
"text": "If z_0 is a limit point of S, then every ϵ-neighborhood of z_0 must contain infinitely many points of S."
},
{
"ref": "2006, Ivan Francis Wilde, Lecture Notes on Complex Analysis, Imperial College Press, page 153",
"text": "As the next example shows, the set of zeros may well have a limit point not belonging to the domain.",
"type": "quotation"
}
],
"glosses": [
"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."
],
"id": "en-limit_point-en-noun-XVY-xzLU",
"links": [
[
"topology",
"topology"
],
[
"topological space",
"topological space"
]
],
"raw_glosses": [
"(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."
],
"related": [
{
"word": "limit"
}
],
"synonyms": [
{
"sense": "point whose every neighborhood contains a point in a given subset",
"word": "accumulation point"
},
{
"sense": "point whose every neighborhood contains a point in a given subset",
"word": "cluster point"
}
],
"topics": [
"mathematics",
"sciences",
"topology"
],
"translations": [
{
"code": "nl",
"lang": "Dutch",
"sense": "point whose every neighborhood contains a point in a given subset",
"word": "verdichtingspunt"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "point whose every neighborhood contains a point in a given subset",
"word": "rajapiste"
},
{
"code": "fr",
"lang": "French",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"masculine"
],
"word": "point d’accumulation"
},
{
"code": "de",
"lang": "German",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"masculine"
],
"word": "Häufungspunkt"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "nekudát gvúl",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"feminine"
],
"word": "נקודת גבול"
},
{
"code": "it",
"lang": "Italian",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"masculine"
],
"word": "punto di accumulazione"
},
{
"code": "pl",
"lang": "Polish",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"masculine"
],
"word": "punkt skupienia"
}
],
"wikipedia": [
"limit point"
]
}
],
"word": "limit point"
}
{
"forms": [
{
"form": "limit points",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "limit point (plural limit points)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "limit"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with quotations",
"en:Topology"
],
"examples": [
{
"ref": "1962 [Ginn and Company], Einar Hille, Analytic Function Theory, Volume 2, 2005, American Mathematical Society, page 19, The function sin ( cot 1/z)",
"text": "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."
},
{
"ref": "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'. […]",
"text": "If z_0 is a limit point of S, then every ϵ-neighborhood of z_0 must contain infinitely many points of S."
},
{
"ref": "2006, Ivan Francis Wilde, Lecture Notes on Complex Analysis, Imperial College Press, page 153",
"text": "As the next example shows, the set of zeros may well have a limit point not belonging to the domain.",
"type": "quotation"
}
],
"glosses": [
"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."
],
"links": [
[
"topology",
"topology"
],
[
"topological space",
"topological space"
]
],
"raw_glosses": [
"(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."
],
"topics": [
"mathematics",
"sciences",
"topology"
],
"wikipedia": [
"limit point"
]
}
],
"synonyms": [
{
"sense": "point whose every neighborhood contains a point in a given subset",
"word": "accumulation point"
},
{
"sense": "point whose every neighborhood contains a point in a given subset",
"word": "cluster point"
}
],
"translations": [
{
"code": "nl",
"lang": "Dutch",
"sense": "point whose every neighborhood contains a point in a given subset",
"word": "verdichtingspunt"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "point whose every neighborhood contains a point in a given subset",
"word": "rajapiste"
},
{
"code": "fr",
"lang": "French",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"masculine"
],
"word": "point d’accumulation"
},
{
"code": "de",
"lang": "German",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"masculine"
],
"word": "Häufungspunkt"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "nekudát gvúl",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"feminine"
],
"word": "נקודת גבול"
},
{
"code": "it",
"lang": "Italian",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"masculine"
],
"word": "punto di accumulazione"
},
{
"code": "pl",
"lang": "Polish",
"sense": "point whose every neighborhood contains a point in a given subset",
"tags": [
"masculine"
],
"word": "punkt skupienia"
}
],
"word": "limit point"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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