See Jordan curve theorem in All languages combined, or Wiktionary
Download JSON data for Jordan curve theorem meaning in English (3.9kB)
{
"head_templates": [
{
"args": {
"1": "en",
"2": "noun",
"head": "Jordan curve theorem"
},
"expansion": "Jordan curve theorem",
"name": "head"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Topology",
"orig": "en:Topology",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "55 45",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "51 49",
"kind": "other",
"name": "English entries with language name categories using raw markup",
"parents": [
"Entries with language name categories using raw markup",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "56 44",
"kind": "other",
"name": "English entries with topic categories using raw markup",
"parents": [
"Entries with topic categories using raw markup",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "57 43",
"kind": "other",
"name": "English terms with non-redundant non-automated sortkeys",
"parents": [
"Terms with non-redundant non-automated sortkeys",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "68 32",
"kind": "topical",
"langcode": "en",
"name": "Curves",
"orig": "en:Curves",
"parents": [
"Shapes",
"Geometry",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w+disamb"
}
],
"examples": [
{
"ref": "1995, William Fulton, Algebraic Topology: A First Course, Springer, page 343",
"text": "There is a vast generalization of the Jordan curve theorem to higher dimensions.",
"type": "quotation"
},
{
"ref": "2001, Theodore Gamelin, Complex Analysis, Springer, page 249",
"text": "The Jordan curve theorem asserts that a simple closed curve in the complex plane divides the plane into exactly two connected components, one bounded (the \"inside\") and the other unbounded (the \"outside\" ).",
"type": "quotation"
},
{
"ref": "2004, Nelson G. Markley, Principles of Differential Equations, Wiley, page 193",
"text": "The principal reason that orbit behavior in the plane is more limited than in higher dimensions is the Jordan curve theorem. Local sections will be the primary tool used to exploit the Jordan curve theorem.",
"type": "quotation"
}
],
"glosses": [
"The theorem that states that a simple closed curve (Jordan curve) divides the plane into precisely two distinct areas."
],
"id": "en-Jordan_curve_theorem-en-noun-MGzb3CeO",
"links": [
[
"topology",
"topology"
],
[
"simple closed curve",
"simple closed curve"
],
[
"Jordan curve",
"Jordan curve"
]
],
"raw_glosses": [
"(topology) The theorem that states that a simple closed curve (Jordan curve) divides the plane into precisely two distinct areas."
],
"topics": [
"mathematics",
"sciences",
"topology"
]
},
{
"categories": [
{
"_dis": "55 45",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "51 49",
"kind": "other",
"name": "English entries with language name categories using raw markup",
"parents": [
"Entries with language name categories using raw markup",
"Entry maintenance"
],
"source": "w+disamb"
}
],
"examples": [
{
"text": "2009, Josef Šlapal, Jordan Curve Theorems with Respect to Certain Pretopologies on ℤ², Srecko Brlek, Christophe Reutenauer, Xavier Provençal (editors), Discrete Geometry for Computer Imagery: 15th IAPR International Conference, Springer, LNCS 5810, page 252,\nSome known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies."
}
],
"glosses": [
"Used other than figuratively or idiomatically: see Jordan curve, theorem."
],
"id": "en-Jordan_curve_theorem-en-noun-yFBx7veM",
"links": [
[
"Jordan curve",
"Jordan curve#English"
],
[
"theorem",
"theorem#English"
]
]
}
],
"word": "Jordan curve theorem"
}
{
"categories": [
"English entries with incorrect language header",
"English entries with language name categories using raw markup",
"English entries with topic categories using raw markup",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with non-redundant non-automated sortkeys",
"en:Curves"
],
"head_templates": [
{
"args": {
"1": "en",
"2": "noun",
"head": "Jordan curve theorem"
},
"expansion": "Jordan curve theorem",
"name": "head"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English terms with quotations",
"en:Topology"
],
"examples": [
{
"ref": "1995, William Fulton, Algebraic Topology: A First Course, Springer, page 343",
"text": "There is a vast generalization of the Jordan curve theorem to higher dimensions.",
"type": "quotation"
},
{
"ref": "2001, Theodore Gamelin, Complex Analysis, Springer, page 249",
"text": "The Jordan curve theorem asserts that a simple closed curve in the complex plane divides the plane into exactly two connected components, one bounded (the \"inside\") and the other unbounded (the \"outside\" ).",
"type": "quotation"
},
{
"ref": "2004, Nelson G. Markley, Principles of Differential Equations, Wiley, page 193",
"text": "The principal reason that orbit behavior in the plane is more limited than in higher dimensions is the Jordan curve theorem. Local sections will be the primary tool used to exploit the Jordan curve theorem.",
"type": "quotation"
}
],
"glosses": [
"The theorem that states that a simple closed curve (Jordan curve) divides the plane into precisely two distinct areas."
],
"links": [
[
"topology",
"topology"
],
[
"simple closed curve",
"simple closed curve"
],
[
"Jordan curve",
"Jordan curve"
]
],
"raw_glosses": [
"(topology) The theorem that states that a simple closed curve (Jordan curve) divides the plane into precisely two distinct areas."
],
"topics": [
"mathematics",
"sciences",
"topology"
]
},
{
"examples": [
{
"text": "2009, Josef Šlapal, Jordan Curve Theorems with Respect to Certain Pretopologies on ℤ², Srecko Brlek, Christophe Reutenauer, Xavier Provençal (editors), Discrete Geometry for Computer Imagery: 15th IAPR International Conference, Springer, LNCS 5810, page 252,\nSome known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies."
}
],
"glosses": [
"Used other than figuratively or idiomatically: see Jordan curve, theorem."
],
"links": [
[
"Jordan curve",
"Jordan curve#English"
],
[
"theorem",
"theorem#English"
]
]
}
],
"word": "Jordan curve theorem"
}
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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.