The Lp-product of ultrametric spaces and the corresponding product of hierarchies

  • Bernard Fichet
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


The L p -product (1 ≤ p ≤ ∞) of r indexed hierarchies is introduced in connection with the L p -product of the corresponding r ultrametric spaces. The Cartesian procluct of two hierarchies appears to be a quasi-hierarchy. Endowed with an index of L p -type (p < ∞). this quasi-hierarchy is in bijection with the L p -product of two ultrametric spaces. The indexed hierarchy associated with the supremum product of r ultrametric spaces is also characterized.


Small Cluster Minimal Element Level Index Ultrametric Space Inclusion Condition 
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Copyright information

© Springer Japan 1998

Authors and Affiliations

  • Bernard Fichet
    • 1
  1. 1.Laboratoire de BiomathématiquesUniversité d’Aix-Marseille IIMarseilleFrance

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