different between surjection vs subjection

English

Etymology

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

Pronunciation

• IPA^(key): /s??(?).d??k.??n/

Noun

surjection (plural surjections)

1. (set theory) A function that is a many-to-one mapping; (formally) Any function ${\displaystyle f:X\rightarrow Y}$ 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 ${\displaystyle A\rightarrow B}$ 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 ${\displaystyle J=\cap _{i}m_{i}}$ be the (irredundant) primary decomposition of ${\displaystyle J}$. We associate to the pair ${\displaystyle (J,\omega )}$ the element ${\displaystyle \textstyle \sum _{i}(m_{i},\omega _{i})\in G}$, 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 ${\displaystyle u:E\rightarrow F}$ (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from ${\displaystyle E/{\text{ker}}(u)}$ to ${\displaystyle F}$ is an isometric isomorphism. Moreover, by the classical open mapping theorem, ${\displaystyle u}$ is a surjection iff the associated mapping from ${\displaystyle E/{\text{ker}}(u)}$ to ${\displaystyle F}$ is an isomorphism.

Synonyms

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

Related terms

• bijection
• injection
• surject

Translations

References

French

Etymology

Formed after bijection and injection.

Pronunciation

• IPA^(key): /sy?.??k.sj??/

Noun

surjection f (plural surjections)

1. (set theory) surjection

Derived terms

• surjectif

English

Etymology

From Anglo-Norman subjectioun, from Old French subjection (Modern French sujétion), from Latin subjecti?.

Pronunciation

Noun

subjection (countable and uncountable, plural subjections)

1. The act of bringing something under the control of something else.
2. The state of being subjected.

Translations

Old French

Alternative forms

Etymology

Borrowed from Latin subjecti?.

Noun

subjection f (oblique plural subjections, nominative singular subjection, nominative plural subjections)

1. subjection; state of being subjected

Descendants

• ? English: subjection
• French: sujétion

References

• subjectiun on the Anglo-Norman On-Line Hub