Systems of germs and theorems of zeros in infinite-dimensional spaces
Complex Variables
2007-05-23 v1 General Mathematics
Abstract
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.
Keywords
Cite
@article{arxiv.math/0612355,
title = {Systems of germs and theorems of zeros in infinite-dimensional spaces},
author = {Dorota Mozyrska and Zbigniew Bartosiewicz},
journal= {arXiv preprint arXiv:math/0612355},
year = {2007}
}
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15 pages