Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 67, Number 2 (2015), 721-751.
On the geometry of sets satisfying the sequence selection property
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.
J. Math. Soc. Japan, Volume 67, Number 2 (2015), 721-751.
First available in Project Euclid: 21 April 2015
Permanent link to this document
Digital Object Identifier
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
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. https://projecteuclid.org/euclid.jmsj/1429624601