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Koike, Satoshi; Paunescu, Laurentiu

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

J. Math. Soc. Japan 67, No. 2, 721-751 (2015).
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.

Cited in 5 Documents

MSC:

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

Keywords:

direction set; transversality; sequence selection property; bi-Lipschitz homeomorphism

Citations:

Zbl 1184.14086
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\textit{S. Koike} and \textit{L. Paunescu}, J. Math. Soc. Japan 67, No. 2, 721--751 (2015; Zbl 1326.14137)
Full Text: DOI arXiv Euclid

References:

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