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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).dʒɛk.ʃən/


surjection (plural surjections)

  1. (set theory) A function that is a many-to-one mapping; (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, 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 termsEdit



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



Borrowing from Latin superiectiō (a throwing over or on; (fig.) an exaggeration, a hyperbole). Compare injection, bijection, with the same second element but different prefixes.


  • IPA(key): /syʁ.ʒɛk.sjɔ̃/
  • (file)


surjection f (plural surjections)

  1. (set theory) surjection

Derived termsEdit