2015/03/03 by José F. Fernando, Fernando, José F.
Mathematics · #14P15 #26E05 #32C20 (secondary) #32C25 (primary) #58A07 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14P15 #msc:26E05 #msc:32C20 #msc:32C25 #msc:58A07
paper · pdf · doi:10.48550/arxiv.1503.00990
33 pages, 6 figures
arxiv created 2015/11/22 · arxiv updated 2015/11/24
In this work we present the concept of amenable C-semianalytic subset of a real analytic manifold M and study the main properties of this type of sets. Amenable C-semianalytic sets can be understood as globally defined semianalytic sets with a neat behavior with respect to Zariski closure. This fact allows us to develop a natural definition of irreducibility and the corresponding theory of irreducible components for amenable C-semianalytic sets. These concepts generalize the parallel ones for: complex algebraic and analytic sets, C-analytic sets, Nash sets and semialgebraic sets.