Additive Subsets

  • Yan Gerard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4040)


Additive subsets have been introduced in the framework of discrete tomography with the underlying notion of x-rays. This notion can be defined from two different ways. We provide in the paper extensions of the two definitions and a proof of their equivalence in a framework where x-rays are replaced by any subsets. It results a pair of dual definitions of additivity cleared out from dispensable assumptions and a proof of their equivalence reduced to a separation theorem.


Convex Hull Convex Cone Normal Linear Space Separation Theorem Polyhedral Cone 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yan Gerard
    • 1
  1. 1.LLAICAuvergne UniversityAubièreFrance

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