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Some topological properties of discrete surfaces

  • Gilles Bertrand
  • Rémy Malgouyres
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1176)

Abstract

A basic property of a simple closed surface is the Jordan's property: the complement of the surface has two connected components. We call backcomponent any such component, and the union of a backcomponent and the surface is called the closure of this back-component. We introduce the notion of strong surface as a surface which satisfies a strong homotopy property: the closure of a back-component is strongly homotopic to that back-component. This means that we can homotopically remove any subset of a strong surface from the closure of a backcomponent. On the basis of some results on homotopy ([2]), and strong homotopy ([3], [4], [5]), we have proved that the simple closed 26-surfaces defined by Morgenthaler and Rosenfeld ([19]), and the simple closed 18-surfaces defined by Malgouyres ([15]) are both strong surfaces. Thus, strong surfaces appear as an interesting generalization of these two notions of a surface.

Keywords

Closed Surface Strong Surface Simple Point Singular Surface Discrete Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Gilles Bertrand
    • 1
  • Rémy Malgouyres
    • 2
  1. 1.Laboratoire PSIESIEE Cité DescartesNoisy-Le-Grand CedexFrance
  2. 2.GREYC, ISMRACaen CedexFrance

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