# What does univoque mean?

This seems to be a french word that is used in English language mathematical papers. It seems to mean something like "unambiguous." What is its technical definition?

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biunivoque is just French for bijective, as far as I know; I don't recall seeing it in English language papers. What example did you have in mind? –  Yemon Choi Jan 26 '10 at 22:19
Caution: I've also seen "biunivoque" used for just "injective" (for example, Grothendieck's Produits tensoriels topologiques et espaces nucleaires). I've also seen "biunivocal" in English (Schaefer's Topological vector spaces, again used for "injective"). –  Loop Space Jan 27 '10 at 9:58
@Andrew: I've also seen univoque used for partial functions; same difference but in the opposite direction. –  François G. Dorais Jan 30 '10 at 19:20

## 2 Answers

Univoque means single-valued, as opposed to multi-valued (multivoque). As Yemon Choi explained, biunivoque means bijective (i.e. single-valued both ways).

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A French English dictionary gives 'univocal' as a translation. I presume the idea is 'with one voice' therefore as suggested 'unambiguous'. The specification of a function is in no two minds as to what image $f(x)$ to assign to $x$. That is a neat image. Thanks for the question. –  Tim Porter Jan 27 '10 at 7:43

So a univoque map is just a function, as opposed to a multivoque map, a relation.

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