2015/11/16 by Iwo Biborski, Biborski, Iwo
Mathematics · #14P15 #32B20 #32S05 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.AG #msc:14P15 #msc:32B20 #msc:32S05
paper · pdf · doi:10.48550/arxiv.1511.05071
arxiv created 2015/11/16 · openalex publication_date 2015/11/16 · arxiv updated 2015/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we show that the equivalences between certain properties of closed subanalytic sets proved by E. Bierstone and P. Milman in \cite[BM-1] hold for closed sets definable in quasianalytic o-minimal structures. In particular we prove that uniform Chevalley estimate implies a stratification by the diagram of initial exponents and further, Zariski semicontinuity of the diagram of initial exponents. We also show that the stratification by the diagram implies Zariski semicontinuity of Hilbert-Samuel function.