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.


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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