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Connective Segmentation Generalized to Arbitrary Complete Lattices

  • Seidon Alsaody
  • Jean Serra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6671)

Abstract

We begin by defining the setup and the framework of connective segmentation. Then we start from a theorem based on connective criteria, established for the power set of an arbitrary set. As the power set is an example of a complete lattice, we formulate and prove an analogue of the theorem for general complete lattices.

Secondly, we consider partial partitions and partial connections. We recall the definitions, and quote a result that gives a characterization of (partial) connections. As a continuation of the work in the first part, we generalize this characterization to complete lattices as well.

Finally we link these two approaches by means of a commutative diagram, in two manners.

Keywords

Connective segmentation complete lattice partial partition block-splitting opening commutative diagram 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Seidon Alsaody
    • 1
    • 2
  • Jean Serra
    • 1
  1. 1.Laboratoire d’Informatique Gaspard-Monge, Equipe AS3I, ESIEE ParisUniversité Paris-EstNoisy le Grand CedexFrance
  2. 2.Department of MathematicsUppsala UniversityUppsalaSweden

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