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As is well known, if E 1, ••• ,Em and Fare vector spaces over the same field, a map A : (Xl' ••. ,xm)~ A(x l , ... ,xm) from E 1 x ... x Em into F is m-linear if for any index i (1::;; i,,;;;; m) and for arbitrary fixed vectors xj E E j (1::;; j::;; m, j ¥- i) the map Xi ~ A(x l , ••• , Xi' •••• x m ) from E, into F is linear. £a(mE, F). fa (Em, F) of all linear maps from Em to F; the subscript a stands for 'algebraic' and indicates that no continuity requirements are involved. fa (mE, F) is symmetric if A(x l , ••• , Xm) = A(Xq(I)' ...

E(U, F). e(U, F) its compact-open topology ;Yo' If U is an open subset of a finite-dimensional J. Horvath / Life and Works of L. Nachbin 49 space, then go is the topology which has been used classically. In the infinite-dimensional case, however, go does not have all the properties one would desire, and therefore several other topologies have been considered on ~(U, F). To explain and motivate the first one of these, the ported topology ([55], [59, Section 8, p. 31]), let me return to the space ~(X; F).

Gil de Lamadrid, J. Nohel, F. Treves, S. Mizohata. Unfortunately in 1970 the owner, Madame Lucienne Treheux died, the apartments were sold as condominiums and became unavailable to visiting mathematicians. Nachbin says in his Houssay-prize acceptance speech: 'I believe that the next four year period 1961-1965 was in many important respects the climax of my career. During the two years of 1961-63 and through the hands of Laurent Schwartz, I was a visiting professor of the University of Paris. ..

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