different between surjection vs subcountable
surjection
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)
- (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.
- 1992, Rowan Garnier, John Taylor, Discrete Mathematics for New Technology, Institute of Physics Publishing, page 220,
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)
- (set theory) surjection
Derived terms
- surjectif
surjection From the web:
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- surjective function
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subcountable
English
Etymology
sub- +? countable
Adjective
subcountable (not comparable)
- (mathematics) Being the target (codomain) of a partial surjection from the natural numbers.
subcountable From the web:
- what uncountable noun
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- what does uncountable mean
- what is uncountable noun and examples
- what is uncountable set
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- what are uncountable and countable nouns
- what is uncountable noun in hindi
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