From Wiktionary, the free dictionary
Jump to navigation Jump to search


English Wikipedia has an article on:
A surjection


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]


  • IPA(key): /sɜː(ɹ)ˈd͡ʒɛk.ʃən/
  • (file)


surjection (plural surjections)

  1. (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.


Related terms[edit]



  1. ^ sŭperjectĭo, Charlton T. Lewis; Charles Short [1879], A Latin Dictionary,



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.



surjection f (plural surjections)

  1. (set theory) surjection

Derived terms[edit]