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Banach spaces in an analytic model of synthetic differential geometry. (English) Zbl 0923.32024
In a previous paper, the authors give an analytic well adapted model of Synthetic Differential Geometry. In this paper, an embedding of the category of open sets of complex Banach spaces and holomorphic maps into this model is constructed and two essential properties are proved. Namely, that this embedding preserves products and that it is consistent with the differential calculus, in the sense that the intrinsic synthetic differential calculus in the topos corresponds to the classical constructions of the theory of infinite dimensional holomorphy. In doing so, some interesting problems in the theory of ideals of analytic functions of several complex variables developed by Cartan are founded and solved.

MSC:
32K99 Generalizations of analytic spaces
51K10 Synthetic differential geometry
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References:
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