surjection

Pronunciation

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Pronunciation

- IPA: /sɜː(ɹ).dʒɛk.ʃən/

**surjection** (*plural* surjections)

- (
*set theory*) A function that is a many-to-one mapping; (*formally*) Any function f: X\rightarrow Y for which for every y \in Y, there is at least one x \in X such that f(x) = y.**1992**, Rowan Garnier, John Taylor,*Discrete Mathematics for New Technology*, IOP Publishing, page 220 ↗,- In some special cases, however, the number of
**surjections**A \rightarrow B can be identified.

- In some special cases, however, the number of
**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 J = \cap_i m_i be the (irredundant) primary decomposition of J. We associate to the pair (J,\omega) the element \textstyle\sum_i (m_i, \omega_i) \in G, where \omega_i is the equivalence class of
**surjections**from L/m_iL \oplus (A/m_i)^{n-1} to m_i/m_i^2 induced by \omega.

- Let J = \cap_i m_i be the (irredundant) primary decomposition of J. We associate to the pair (J,\omega) the element \textstyle\sum_i (m_i, \omega_i) \in G, where \omega_i is the equivalence class of
**2003**, Gilles Pisier,*Introduction to Operator Space Theory*, Cambridge University Press, page 43 ↗,- In Banach space theory, a mapping u: E \rightarrow F (between Banach spaces) is called a metric
**surjection**if it is onto and if the associated mapping from E / \text{ker}(u) to F is an isometric isomorphism. Moreover, by the classical open mapping theorem, u is a**surjection**iff the associated mapping from E/ \text{ker}(u) to F is an isomorphism.

- In Banach space theory, a mapping u: E \rightarrow F (between Banach spaces) is called a metric

- (
*function that is a many-to-one mapping*) surjective function

- French: surjection
- German: Surjektion
- Italian: suriezione
- Portuguese: sobrejeção
- Russian: сюръе́кция
- Spanish: función sobreyectiva

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.002