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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2$\begingroup$ 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? $\endgroup$– Yemon ChoiJan 26, 2010 at 22:19
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2$\begingroup$ 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"). $\endgroup$– Andrew StaceyJan 27, 2010 at 9:58
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$\begingroup$ @Andrew: I've also seen univoque used for partial functions; same difference but in the opposite direction. $\endgroup$– François G. DoraisJan 30, 2010 at 19:20
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2 Answers
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Univoque means single-valued, as opposed to multi-valued (multivoque). As Yemon Choi explained, biunivoque means bijective (i.e. single-valued both ways).
answered Jan 26, 2010 at 22:52
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$\begingroup$ 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. $\endgroup$ Jan 27, 2010 at 7:43
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So a univoque map is just a function, as opposed to a multivoque map, a relation.
