On the geometry of sets satisfying the sequence selection property. (English) Zbl 1326.14137

Summary: In this paper we study fundamental directional properties of sets under the assumption of condition (SSP) (introduced in [the authors, Ann. Inst. Fourier 59, No. 6, 2445–2467 (2009; Zbl 1184.14086)]). We show several transversality theorems in the singular case and an (SSP)-structure preserving theorem. As a geometric illustration, our transversality results are used to prove several facts concerning complex analytic varieties in 3.3. Also, using our results on sets with condition (SSP), we give a classification of spirals in the appendix 5.
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.


14P15 Real-analytic and semi-analytic sets
32B20 Semi-analytic sets, subanalytic sets, and generalizations
57R45 Singularities of differentiable mappings in differential topology


Zbl 1184.14086
Full Text: DOI arXiv Euclid


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