surjection en · NOUN
Pronunciation
Etymology
From French surjection, introduced by the Bourbaki group in their treatise Éléments de mathématique. Ultimately borrowed from Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”).
Meanings
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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.
In Banach space theory, a mapping u#58;E#92;rightarrowF (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from E#47;#92;text#123;ker#125;(u) to F is an isometric isomorphism. Moreover, by the classical open mapping theorem, u is a surjection iff the associated mapping from E#47;#92;text#123;ker#125;(u) to F is an isomorphism.
2003, Gilles Pisier, Introduction to Operator Space Theory, Cambridge University Press, page 43:In some special cases, however, the number of surjections A#92;rightarrowB can be identified.
1992, Rowan Garnier, John Taylor, Discrete Mathematics for New Technology, Institute of Physics Publishing, page 220:Let J#61;#92;cap#95;im#95;i be the (irredundant) primary decomposition of J. We associate to the pair (J,#92;omega) the element #92;textstyle#92;sum#95;i(m#95;i,#92;omega#95;i)#92;inG, where #92;omega#95;i is the equivalence class of surjections from L#47;m#95;iL#92;oplus(A#47;m#95;i)#123;n-1#125; to m#95;i#47;m#95;i² induced by #92;omega.
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:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| surjections | Number=Plur | lexicographic |
Relateds
bijection · injection · surject
Synonyms
onto function · surjective function
Translations (25)
ko 전사 (function that is a many-to-one mapping) · ca funció exhaustiva (function that is a many-to-one mapping) · el επίρριψη (function that is a many-to-one mapping) · bg сюрекция (function that is a many-to-one mapping) · ro funcție surjectivă (function that is a many-to-one mapping) · es función sobreyectiva (function that is a many-to-one mapping) · sh surjekcija (function that is a many-to-one mapping) · io surjekto (function that is a many-to-one mapping) · sv surjektion (function that is a many-to-one mapping) · pt sobrejeção (function that is a many-to-one mapping) · de Surjektion (function that is a many-to-one mapping) · ru сюръе́кция (function that is a many-to-one mapping) · cmn 满射 (function that is a many-to-one mapping) · vi toàn ánh (function that is a many-to-one mapping) · ro surjecție (function that is a many-to-one mapping) · de surjektive Funktion (function that is a many-to-one mapping) · pl suriekcja (function that is a many-to-one mapping) · fr surjection (function that is a many-to-one mapping) · et sürjektsioon (function that is a many-to-one mapping) · cs surjekce (function that is a many-to-one mapping) · sk surjekcia (function that is a many-to-one mapping) · et surjection (function that is a many-to-one mapping) · it suriezione (function that is a many-to-one mapping) · ja 全射 (function that is a many-to-one mapping) · fi surjektio (function that is a many-to-one mapping)
wikipedia: Nicolas Bourbaki · wikipedia: Éléments de mathématique