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Biclosed Binary Relations and Galois Connections

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Abstract

Given two closure spaces (E,ϕ) and (E′,ϕ′), a relation R⊒E×E′ is said biclosed if every row of its matrix representation corresponds to a closed subset of E′, and every column to a closed subset of E. An isomorphism between, on the one hand, the set of all biclosed relations and, on the other hand, the set of all Galois connections between the two lattices of closed sets is established. Several computational applications are derived from this result.

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Authors and Affiliations

  1. CERMSEM, 106-112 bd de l'Hopital, 75647, Paris Cedex 13, France

    Florent Domenach

  2. CAMS, 54 bd Raspail, 75006, Paris, France

    Bruno Leclerc

Authors
  1. Florent Domenach
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  2. Bruno Leclerc
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Domenach, F., Leclerc, B. Biclosed Binary Relations and Galois Connections. Order 18, 89–104 (2001). https://doi.org/10.1023/A:1010662327346

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