, Volume 33, Issue 3, pp 503–516 | Cite as

Weakening Additivity in Adjoining Closures

  • Isabella Mastroeni
  • Roberto Giacobazzi


In this paper, we weaken the conditions for the existence of adjoint closure operators, going beyond the standard requirement of additivity/co-additivity. We consider the notion of join-uniform (lower) closure operators, introduced in computer science, in order to model perfect lossless compression in transformations acting on complete lattices. Starting from Janowitz’s characterization of residuated closure operators, we show that join-uniformity perfectly weakens additivity in the construction of adjoint closures, and this is indeed the weakest property for this to hold. We conclude by characterizing the set of all join-uniform lower closure operators as fix-points of a function defined on the set of all lower closures of a complete lattice.


Residuated closures Uniformity Sdjoint functions 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di VeronaVeronaItaly
  2. 2.IMDEA Software InstituteMadridSpain

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