surjectionとは 意味・読み方・使い方

語源

From French surjection, introduced by the Bourbaki group in their treatise Éléments de mathématique. Ultimately borrowed from Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”).

発音

• IPA: /sɜː(ɹ)ˈd͡ʒɛk.ʃən/

名詞

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 ${\displaystyle f:X\to Y}$ for which for every ${\displaystyle y\in Y}$, there is at least one ${\displaystyle x\in X}$ such that ${\displaystyle f(x)=y}$.
   • 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 ${\displaystyle A\to B}$ 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 ${\displaystyle J={\cap }_i{m}_i}$ be the (irredundant) primary decomposition of ${\displaystyle J}$. We associate to the pair ${\displaystyle (J,\omega )}$ the element ${\displaystyle {\sum }_i(m_i,{\omega }_i)\in G}$, where ${\displaystyle {\omega }_i}$ is the equivalence class of surjections from ${\displaystyle L/m_{i}L\oplus (A/m_i{)}^{n-1}}$ to ${\displaystyle m_i/m_i^2}$ induced by ${\displaystyle \omega }$.

   • 2003, Gilles Pisier, Introduction to Operator Space Theory, Cambridge University Press, page 43:

     In Banach space theory, a mapping ${\displaystyle u:E\to F}$ (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from ${\displaystyle E/\text{<a href="https://ejje.weblio.jp/content/ker" title="kerの意味" class="crosslink">ker</a>}(u)}$ to ${\displaystyle F}$ is an isometric isomorphism. Moreover, by the classical open mapping theorem, ${\displaystyle u}$ is a surjection iff the associated mapping from ${\displaystyle E/\text{<a href="https://ejje.weblio.jp/content/ker" title="kerの意味" class="crosslink">ker</a>}(u)}$ to ${\displaystyle F}$ is an isomorphism.

同意語

• surjective function
• onto function

関連する語

• bijection
• injection
• surject

参照