2012/01/08 by Satoshi Koike, Koike, Satoshi, Laurentiu Paunescu +2
Engineering · Mathematics · #14P15 #32B20 (Primary) 57R45 (Secondary) #Advanced Numerical Analysis Techniques #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14P15 #msc:32B20 #msc:57R45
paper · pdf · doi:10.48550/arxiv.1201.1669
28 pages, 3 figures included
openalex publication_date 2012/01/08 · arxiv created 2013/09/23 · arxiv updated 2013/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study fundamental directional properties of sets under the assumption of condition (SSP) (introduced in a previous paper). We show several transversality theorems in the singular case and an (SSP)-structure preserving theorem. As an illustration, our transversality results are used to prove several facts concerning complex analytic varieties. The (SSP)-property is most suitable for understanding transversality in the Lipschitz category. This property is shared by a large class of sets, in particular by subanalytic sets or by definable sets in an o-minimal structure.