surjection
English edit
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
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)