Open Access
April, 2015 On the geometry of sets satisfying the sequence selection property
Satoshi KOIKE, Laurentiu PAUNESCU
J. Math. Soc. Japan 67(2): 721-751 (April, 2015). DOI: 10.2969/jmsj/06720721


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.


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Satoshi KOIKE. Laurentiu PAUNESCU. "On the geometry of sets satisfying the sequence selection property." J. Math. Soc. Japan 67 (2) 721 - 751, April, 2015.


Published: April, 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1326.14137
MathSciNet: MR3340193
Digital Object Identifier: 10.2969/jmsj/06720721

Primary: 14P15 , 32B20
Secondary: 57R45

Keywords: bi-Lipschitz homeomorphism , direction set , sequence selection property , transversality

Rights: Copyright © 2015 Mathematical Society of Japan

Vol.67 • No. 2 • April, 2015
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