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In this paper, we have described a denotational model of Intuitionist LinearLogic which is also a differential category. Formulas are interpreted asMackey-complete topological vector space and linear proofs are interpreted bybounded linear functions. So as to interpret non-linear proofs of Linear Logic,we have used a notion of power series between Mackey-complete spaces,generalizing the notion of entire functions in C. Finally, we have obtained aquantitative model of Intuitionist Differential Linear Logic, where thesyntactic differentiation correspond to the usual one and where theinterpretations of proofs satisfy a Taylor expansion decomposition.

Mackey-complete spaces and power series -- A topological model of Differential Linear Logic