Decomposition of sets in real algebraic geometry
Algebraic Geometry
2018-07-04 v2
Abstract
We present a new notion of decomposition of semialgebraic sets by introducing a mode of irreducibility based on arc-analytic functions. The result is a refinement of the decomposition of such sets with respect to the Zariski topology as well as a refinement of the decomposition in each of the recent approaches based on Nash and continuous rational functions. In addition, by pairing the ring of arc-analytic functions with semialgebraic sets, we obtain a theory of algebraic geometry equipped with strong tools such as the Identity Principle and the Nullstellensatz.
Cite
@article{arxiv.1704.08965,
title = {Decomposition of sets in real algebraic geometry},
author = {Hadi Seyedinejad},
journal= {arXiv preprint arXiv:1704.08965},
year = {2018}
}
Comments
Requires thorough corrections (and project inactive for the foreseeable future)