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In french, there is a word for what's called an "application" that can be bijective, injective or surjective, in english I only see the word "function".

In french, an application is defined as a relation between two sets, where each element of the first set is linked to a unique element of the second set, is there any word more precise than a function for this definition in English?

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    The term "function" signifies exactly that. – 2017-01-29
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    @OpenBall Thank you !! Its funny that we are using two different words in french! – 2017-01-29
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    Related: http://math.stackexchange.com/questions/95741/is-there-any-difference-between-mapping-and-function I suspect in fact in French they also define the same notion. – 2017-01-29
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    You're welcome. Not too funny, as we also have the name "mapping". – 2017-01-29
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    @Wolfram Oh I see... well yes, the term used probably depends on the context of what we are studying... – 2017-01-29
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    *Application*, *map* and *function* are synonyms, at least in Italian, French and English. In Italian we use different terms according to the domains of such objects: real numbers, spaces of functions, geometric subspaces etc. – 2017-01-29
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    Also in Russian we have "отображение" aka mapping and "функция" aka "function". – 2017-01-29
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    See [Application](https://fr.wikipedia.org/wiki/Application_(math%C3%A9matiques)) : It seems to me that math English does not distinguish between the two cases : *total* (defined for every element of the *source*) and not. See also the [ref to Bourbaki](https://fr.wikipedia.org/wiki/Application_(math%C3%A9matiques)#Fonction_et_application). – 2017-01-29
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    @MauroALLEGRANZA Oh so there is a small difference then... but I see that in practice it does not matter much! – 2017-01-29
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    The original French Bourbaki [E II.14](https://books.google.it/books?id=VDGifaOQogcC&printsec=frontcover) has *fonction* and *application* : "une fonction $f$ [de $A$ dans $B$] dont l'ensemble de départ est egal à $A$ ..." – 2017-01-29
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    The (1968) English transl ([page 81](https://books.google.it/books?id=IL-SI67hjI4C&pg=PA81)) has respectively : *function* and *mapping of* $A$ *into* $B$". – 2017-01-29

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