On the Geometry of sets satisfying the Sequence Selection Property

Details On the Geometry of sets satisfying the Sequence Selection Property On the Geometry of sets satisfying the Sequence Selection Property

2012-01-08

arxiv.org/abs/1201.1669v1

Mathematics

Algebraic Geometry

28 pages, 3 figures included

Scientific paper

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.

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