2010/11/18 by Daniel Barlet, Barlet, Daniel, Teresa Monteiro Fernandes +1
Mathematics · #14P15 #32B20 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14P15 #msc:32B20
paper · pdf · doi:10.48550/arxiv.1011.4208
Main theorem improved, added references, corrected typos, revised some arguments, to appear in Studia Mathematica
arxiv created 2011/04/08 · arxiv updated 2011/04/11
By open neighbourhood of an open subset Ω of ℝn we mean an open subset Ω' of ℂn such that ℝn∩Ω'=Ω. A well known result of H. Grauert implies that any open subset of ℝn admits a fundamental system of Stein open neighbourhoods in ℂn. Another way to state this property is to say that each open subset of ℝn is Stein. We shall prove a similar result in the subanalytic category, so, under the assumption that Ω is a subanalytic relatively compact open subset in a real analytic manifold, we show that Ω admits a fundamental system of subanalytic Stein open neighbourhoods in any of its complexifications.