Journal of the Mathematical Society of Japan

On the geometry of sets satisfying the sequence selection property

Satoshi KOIKE and Laurentiu PAUNESCU

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In this paper we study fundamental directional properties of sets under the assumption of condition (SSP) (introduced in [ 3]). 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.

Article information

J. Math. Soc. Japan, Volume 67, Number 2 (2015), 721-751.

First available in Project Euclid: 21 April 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14P15: Real analytic and semianalytic sets [See also 32B20, 32C05] 32B20: Semi-analytic sets and subanalytic sets [See also 14P15]
Secondary: 57R45: Singularities of differentiable mappings

direction set transversality sequence selection property bi-Lipschitz homeomorphism


KOIKE, Satoshi; PAUNESCU, Laurentiu. On the geometry of sets satisfying the sequence selection property. J. Math. Soc. Japan 67 (2015), no. 2, 721--751. doi:10.2969/jmsj/06720721.

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