Hausdorff Discretizations of Algebraic Sets and Diophantine Sets

  • Mohamed Tajine
  • Christian Ronse
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)


This paper is a continuation of our works [12],[13],[15],[16],[17],[18] [21]

We study the properties of Hausdorff discretizations of algebraic sets. Actually we give some decidable and undecidable properties concerning Hausdorff discretizations of algebraic sets and we prove that some Hausdorff discretizations of algebraic sets are diophantine sets. We refine the last results for algebraic curves and more precisely for straight lines.


Algebraic set diophantine set Hausdorff discretization homogeneous metric 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Mohamed Tajine
    • 1
  • Christian Ronse
    • 1
  1. 1.Laboratoire des Sciences de l’Imagede l’Informatique et de la Télédétection (LSIIT, UPRES-A CNRS 7005)IllkirchFrance

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