surjection
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English
[edit]![](http://178.128.105.246/cars-http-upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Surjection.svg/220px-Surjection.svg.png)
Etymology
[edit]From French surjection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique. Ultimately borrowed from Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”).[1]
Pronunciation
[edit]- IPA(key): /sɜː(ɹ)ˈd͡ʒɛk.ʃən/
Audio (Southern England): (file)
Noun
[edit]surjection (plural surjections)
- (set theory) A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function for which for every , there is at least one such that .
- 1992, Rowan Garnier, John Taylor, Discrete Mathematics for New Technology, Institute of Physics Publishing, page 220:
- In some special cases, however, the number of surjections can be identified.
- 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:
- Let be the (irredundant) primary decomposition of . We associate to the pair the element , where is the equivalence class of surjections from to induced by .
- 2003, Gilles Pisier, Introduction to Operator Space Theory, Cambridge University Press, page 43:
- In Banach space theory, a mapping (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from to is an isometric isomorphism. Moreover, by the classical open mapping theorem, is a surjection iff the associated mapping from to is an isomorphism.
Synonyms
[edit]Related terms
[edit]Translations
[edit]function that is a many-to-one mapping
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References
[edit]- ^ sŭperjectĭo, Charlton T. Lewis; Charles Short [1879], A Latin Dictionary, uchicago.edu
French
[edit]Etymology
[edit]Borrowing from Latin superiectiōnem (“a throwing over or on; (figuratively) an exaggeration, a hyperbole”). Compare injection, bijection, with the same second element but different prefixes.
Pronunciation
[edit]Noun
[edit]surjection f (plural surjections)
Derived terms
[edit]Categories:
- English terms derived from French
- English coinages
- English terms borrowed from Latin
- English terms derived from Latin
- English 3-syllable words
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- English lemmas
- English nouns
- English countable nouns
- en:Set theory
- en:Functions
- English terms with quotations
- French terms borrowed from Latin
- French terms derived from Latin
- French 3-syllable words
- French terms with IPA pronunciation
- French terms with audio links
- French lemmas
- French nouns
- French countable nouns
- French feminine nouns
- fr:Set theory