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A surjection


From French surjection, introduced by Nicolas Bourbaki in his treatise Éléments de mathématique.


  • 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 terms[edit]




Formed after bijection and injection.


surjection f (plural surjections)

  1. (set theory) surjection

Derived terms[edit]