Systems of germs and theorems of zeros in infinite-dimensional spaces

Details Systems of germs and theorems of zeros in infinite-dimensional spaces Systems of germs and theorems of zeros in infinite-dimensional spaces

2006-12-13

arxiv.org/abs/math/0612355v1

Mathematics

Complex Variables

15 pages

Scientific paper

Systems of germs of sets in infinite-dimensional spaces are introduced and studied. Such a system corresponds to a local zero-set of an ideal of the ring of analytic functions of infinite number of variables. Conversely, this system of germs defines the ideal of germs of analytic functions vanishing on it. A theorem of zeros is proved, stating that this ideal is the radical (in the complex case) or real radical (in the real case) of the initial ideal.

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