See surjection in All languages combined, or Wiktionary
Download JSON data for surjection meaning in English (7.6kB)
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"3": "superiaciō",
"4": "superiectiō",
"5": "a throwing over or on; (fig.) an exaggeration, a hyperbole"
},
"expansion": "Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”)",
"name": "bor"
}
],
"etymology_text": "From French surjection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.\nUltimately borrowed from Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”).",
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"ref": "1992, Rowan Garnier, John Taylor, Discrete Mathematics for New Technology, Institute of Physics Publishing, page 220",
"text": "In some special cases, however, the number of surjections A#x5C;rightarrowB can be identified.",
"type": "quotation"
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{
"ref": "1999, M. Pavaman Murthy, “A survey of obstruction theory for projective modules of top rank”, in Tsit-Yuen Lam, Andy R. Magid, editors, Algebra, K-theory, Groups, and Education: On the Occasion of Hyman Bass's 65th Birthday, American Mathematical Society, page 168",
"text": "Let J#x3D;#x5C;cap#x5F;im#x5F;i be the (irredundant) primary decomposition of J. We associate to the pair (J,#x5C;omega) the element #x5C;textstyle#x5C;sum#x5F;i(m#x5F;i,#x5C;omega#x5F;i)#x5C;inG, where #x5C;omega#x5F;i is the equivalence class of surjections from L#x2F;m#x5F;iL#x5C;oplus(A#x2F;m#x5F;i)#x7B;n-1#x7D; to m#x5F;i#x2F;m#x5F;i² induced by #x5C;omega.",
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"ref": "2003, Gilles Pisier, Introduction to Operator Space Theory, Cambridge University Press, page 43",
"text": "In Banach space theory, a mapping u#x3A;E#x5C;rightarrowF (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from E#x2F;#x5C;text#x7B;ker#x7D;(u) to F is an isometric isomorphism. Moreover, by the classical open mapping theorem, u is a surjection iff the associated mapping from E#x2F;#x5C;text#x7B;ker#x7D;(u) to F is an isomorphism.",
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"A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function f:X→Y for which for every y∈Y, there is at least one x∈X such that f(x)=y."
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"id": "en-surjection-en-noun--MQY-ReP",
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"(set theory) A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function f:X→Y for which for every y∈Y, there is at least one x∈X such that f(x)=y."
],
"related": [
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"word": "bijection"
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{
"word": "injection"
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{
"word": "surject"
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"word": "surjective function"
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{
"word": "onto function"
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{
"code": "ca",
"lang": "Catalan",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "funció exhaustiva"
},
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"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "mǎnshè",
"sense": "function that is a many-to-one mapping",
"word": "满射"
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"code": "cs",
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"sense": "function that is a many-to-one mapping",
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"sense": "function that is a many-to-one mapping",
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"code": "et",
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"sense": "function that is a many-to-one mapping",
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"sense": "function that is a many-to-one mapping",
"word": "surjektio"
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"lang": "French",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
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"word": "surjection"
},
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"lang": "German",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "Surjektion"
},
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"code": "de",
"lang": "German",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "surjektive Funktion"
},
{
"code": "el",
"lang": "Greek",
"roman": "epírripsi",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
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"word": "επίρριψη"
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"code": "io",
"lang": "Ido",
"sense": "function that is a many-to-one mapping",
"word": "surjekto"
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{
"code": "it",
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"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
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"word": "suriezione"
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{
"code": "ja",
"lang": "Japanese",
"roman": "zensha",
"sense": "function that is a many-to-one mapping",
"word": "全射"
},
{
"alt": "全射",
"code": "ko",
"lang": "Korean",
"roman": "jeonsa",
"sense": "function that is a many-to-one mapping",
"word": "전사"
},
{
"code": "pl",
"lang": "Polish",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "suriekcja"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
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"word": "sobrejeção"
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{
"code": "ro",
"lang": "Romanian",
"sense": "function that is a many-to-one mapping",
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{
"code": "ro",
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"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
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"word": "funcție surjectivă"
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{
"code": "ru",
"lang": "Russian",
"roman": "sjurʺjékcija",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "сюръе́кция"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
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"word": "surjekcija"
},
{
"code": "es",
"lang": "Spanish",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "función sobreyectiva"
},
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"code": "sv",
"lang": "Swedish",
"sense": "function that is a many-to-one mapping",
"tags": [
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"word": "surjektion"
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},
"expansion": "Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”)",
"name": "bor"
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],
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{
"word": "surject"
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"ref": "1992, Rowan Garnier, John Taylor, Discrete Mathematics for New Technology, Institute of Physics Publishing, page 220",
"text": "In some special cases, however, the number of surjections A#x5C;rightarrowB can be identified.",
"type": "quotation"
},
{
"ref": "1999, M. Pavaman Murthy, “A survey of obstruction theory for projective modules of top rank”, in Tsit-Yuen Lam, Andy R. Magid, editors, Algebra, K-theory, Groups, and Education: On the Occasion of Hyman Bass's 65th Birthday, American Mathematical Society, page 168",
"text": "Let J#x3D;#x5C;cap#x5F;im#x5F;i be the (irredundant) primary decomposition of J. We associate to the pair (J,#x5C;omega) the element #x5C;textstyle#x5C;sum#x5F;i(m#x5F;i,#x5C;omega#x5F;i)#x5C;inG, where #x5C;omega#x5F;i is the equivalence class of surjections from L#x2F;m#x5F;iL#x5C;oplus(A#x2F;m#x5F;i)#x7B;n-1#x7D; to m#x5F;i#x2F;m#x5F;i² induced by #x5C;omega.",
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{
"ref": "2003, Gilles Pisier, Introduction to Operator Space Theory, Cambridge University Press, page 43",
"text": "In Banach space theory, a mapping u#x3A;E#x5C;rightarrowF (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from E#x2F;#x5C;text#x7B;ker#x7D;(u) to F is an isometric isomorphism. Moreover, by the classical open mapping theorem, u is a surjection iff the associated mapping from E#x2F;#x5C;text#x7B;ker#x7D;(u) to F is an isomorphism.",
"type": "quotation"
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"A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function f:X→Y for which for every y∈Y, there is at least one x∈X such that f(x)=y."
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"(set theory) A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function f:X→Y for which for every y∈Y, there is at least one x∈X such that f(x)=y."
],
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{
"code": "ca",
"lang": "Catalan",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "funció exhaustiva"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "mǎnshè",
"sense": "function that is a many-to-one mapping",
"word": "满射"
},
{
"code": "cs",
"lang": "Czech",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "surjekce"
},
{
"code": "et",
"lang": "Estonian",
"sense": "function that is a many-to-one mapping",
"word": "sürjektsioon"
},
{
"code": "et",
"lang": "Estonian",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "surjection"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "function that is a many-to-one mapping",
"word": "surjektio"
},
{
"code": "fr",
"lang": "French",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "surjection"
},
{
"code": "de",
"lang": "German",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "Surjektion"
},
{
"code": "de",
"lang": "German",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "surjektive Funktion"
},
{
"code": "el",
"lang": "Greek",
"roman": "epírripsi",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "επίρριψη"
},
{
"code": "io",
"lang": "Ido",
"sense": "function that is a many-to-one mapping",
"word": "surjekto"
},
{
"code": "it",
"lang": "Italian",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "suriezione"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "zensha",
"sense": "function that is a many-to-one mapping",
"word": "全射"
},
{
"alt": "全射",
"code": "ko",
"lang": "Korean",
"roman": "jeonsa",
"sense": "function that is a many-to-one mapping",
"word": "전사"
},
{
"code": "pl",
"lang": "Polish",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "suriekcja"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "sobrejeção"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "function that is a many-to-one mapping",
"tags": [
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"word": "surjecție"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "funcție surjectivă"
},
{
"code": "ru",
"lang": "Russian",
"roman": "sjurʺjékcija",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "сюръе́кция"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "surjekcija"
},
{
"code": "es",
"lang": "Spanish",
"sense": "function that is a many-to-one mapping",
"tags": [
"feminine"
],
"word": "función sobreyectiva"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "function that is a many-to-one mapping",
"tags": [
"common-gender"
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"word": "surjektion"
}
],
"word": "surjection"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-06 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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