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What is the modern concept (term) for "separating duality" (dualité séparante in french) in the sense of Bourbaki (TVS Ch II § 6) as explained in the following ? 

Let E, F be two k-vector spaces and B : E x F --> k a bilinear form, one 
says that B puts F,G in duality. The duality is separating in E iff for 
all x\not=0 in E it exists y\in F such that B(x,y)\not=0. It is separating 
in F iff for all y\not=0 in F il exists x\in E such that B(x,y)\not=0. 

The duality is called separating iff it is separating in E and F.

I am currently using this notion in the context of Hopf algebras (where it is not usual).

Anyone knows the modern terms ? links ?

Thanks in advance.

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    $\begingroup$ The 1987 translation by Eggleston & Madan renders it exactly as you do: "We say that the duality defined by $B$ is separating in $F$ (resp. in $G$) if ..." $\endgroup$
    – Francois Ziegler
    Aug 23, 2014 at 19:32
  • $\begingroup$ @François Ziegler Thank you. I have this translation but would like to know if these terms are still up-to-date. $\endgroup$
    – Duchamp Gérard H. E.
    Aug 23, 2014 at 22:04
  • $\begingroup$ Yes, I understand. That's why I made this a comment and not an answer. $\endgroup$
    – Francois Ziegler
    Aug 23, 2014 at 22:09
  • $\begingroup$ @François Ziegler : Point taken. $\endgroup$
    – Duchamp Gérard H. E.
    Aug 23, 2014 at 22:39
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    $\begingroup$ Another notion often used (in particular, in the study of duals of locally convex spaces) is the following: a family $\alpha_x$ of linear, (continuous) functionals on $E$ "separates points of $E$" if for all non-zero $e \in E$ there exists $x$ such that $\alpha_x(e) \neq 0$. So I think "duality separating points" should work also. $\endgroup$
    – Tobias Diez
    Aug 24, 2014 at 9:07

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