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A duality for involutive bisemilattices. (English) Zbl 1475.06001

In this paper, the authors provide a duality between the categories of involutive bisemilattices and GR spaces, which are compact totally disconnected partially ordered left normal bands with constants. Involutive bisemilattices are representable as Plonka sums over a direct system of Boolean algebras. Using this, the authors describe the dual spaces of an involutive bisemilattice inverse systems of Stone spaces. They generalize the Gierz and Romanowska duality for GR spaces with involution as an additional operation [G. Gierz and A. Romanowska, J. Aust. Math. Soc., Ser. A 51, No. 2, 247–275 (1991; Zbl 0751.06008)].

MSC:

06A12 Semilattices
08C20 Natural dualities for classes of algebras
06E15 Stone spaces (Boolean spaces) and related structures
22A30 Other topological algebraic systems and their representations

Citations:

Zbl 0751.06008
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References:

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