Andrej Bauer in Karin Cvetko-Vah: Stoneova dualnost za poševne Boolove algebre
Naslov: Stoneova dualnost za poševne Boolove algebre
Povzetek: Predstavila bova posplošitev Stoneove dualnosti za (komutativne) Boolove algebre na poševne Boolove algebre. Osnovna verzija dualnosti je kontravariantna ekvivalenca kategorij (s primerno izbranimi morfizmi) presečnih poševnih Boolovih algeber in nekaterih snopov nad Boolovimi prostori (Hausdorffovi, lokalno kompaktni in 0-dimenzionalni). Predstavila bova tudi nekatere razširitve dualnosti in jo uporabila za rešitev odprtega problema v teoriji poševnih Boolovih algeber.
Title: Stone duality for skew Boolean algebras
Abstract: We will present a generalization of Stone duality for (commutative) Boolean algebras to skew Boolean algebras. The basic duality states a contravariant equivalence of the categories (with suitably chosen morphisms) of skew Boolean algebras with intersections and certain sheaves of Boolean spaces (Hausdorff, locally compact and 0-dimensional). We will also present some extensions of the duality and use it for a solution of an open problem in the theory of skew Boolean algebras.
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