(SSP) geometry with directional homeomorphisms

Satoshi Koike and Laurentiu Paunescu

Journal of Singularities
volume 13 (2015), 169-178

Received 23 September 2013. Received in revised form 22 July 2014.

DOI: 10.5427/jsing.2015.13i

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In a previous paper we discussed several directional properties of sets satisfying the sequence selection property, denoted by (SSP) for short, and developed the (SSP) geometry via bi-Lipschitz transformations. In this paper we introduce the notion of directional homeomorphism and show that we can develop also the (SSP) geometry with directional transformations. For many important results proved earlier for bi-Lipschitz homeomorphisms we describe the analogues for directional homeomorphisms as well.


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

Mathematical Subject Classification:

Primary 14P15, 32B20; Secondary 57R45

Author(s) information:

Satoshi Koike Laurentiu Paunescu
Department of Mathematics School of Mathematics and Statistics
Hyogo University of Teacher Education University of Sydney
Kato, Hyogo 673-1494, Japan Sydney, NSW, 2006, Australia
email: koike@hyogo-u.ac.jp email: laurent@maths.usyd.edu.au