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Duality for quasilattices and Galois connections. (English) Zbl 1425.06003

Summary: The primary goal of the paper is to establish a duality for quasilattices. The main ingredients are duality for semilattices and their representations, the structural analysis of quasilattices as Płonka sums of lattices, and the duality for lattices developed by C. Hartonas and J. M. Dunn [Algebra Univers. 37, No. 3, 391–401 (1997; Zbl 0902.06008)]. Lattice duality treats the identity function on a lattice as a Galois connection between its meet and join semilattice reducts, and then invokes a duality between Galois connections and polarities. A second goal of the paper is a further examination of this latter duality, using the concept of a pairing to provide an algebraic equivalent to the relational structure of a polarity.

MSC:

06D50 Lattices and duality
06A15 Galois correspondences, closure operators (in relation to ordered sets)
06A11 Algebraic aspects of posets

Citations:

Zbl 0902.06008
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