Boolean algebraBoolean spaceStone dualityétalé spacepresheaf of setsright normal bandPrimary 06E75Secondary 06E1518B30We describe right-hand skew Boolean algebras in terms of a class of presheaves of sets over Boolean algebras called Boolean sets, and prove a duality theorem between Boolean sets ...
These results indicate how to proceed to find models of set theory in which Sierpiński's duality principle fails. By the Bartoszy' nski-Raisonnier-Stern theorem, add(N) ≤ cov(M) is true in any model of set theory. Thus, if the Sierpiński duality principle were true in all models of...
Stone's representation theorem for boolean algebras, the foundation for the so called Stone duality between boolean algebras and Stone spaces, manifests a tight connection between logic and topology. It has thus become an ubiquitous tool in various areas of theoretical computer science, not only in...
The next lemma, that we state for further reference, can be proved with arguments quite similar to those used in the proof of [27, Theorem 3.8]. Lemma 2.1 Let S be a subalgebra of the MV-algebra Γ(G,u), and H be the sub-ℓ-group of G generated by S. Then S=Γ(H,u). ...
Topology,Lattices,Boolean algebra,Geometry,Computer science,IndexesWe propose the concept of topological dualizability as the condition of possibility of Stone duality, and thereby give a non-Hausdorff extension of the primal duality theorem in natural duality theory in universal algebra. The primal ...
In particular, a Stone-type duality theorem for the category of compact Hausdorff spaces and open maps is obtained. Some equivalence theorems for these four categories are stated as well; two of them generalize the Fedorchuk equivalence theorem [V.V. Fedorchuk, Boolean δ-algebras and quasi-open...
Local contact algebraCompact spacesLocally compact spacesSkeletal maps(Quasi-)open perfect maps(Quasi-)open mapsPerfect mapsDualityEquivalenceGeneralizing duality theorem of V.V. Fedorchuk [V.V. Fedorchuk, Boolean δ-algebras and quasi-open mappings, Sibirsk. Mat. Zh. 14 (5) (1973) 1088–1099;...
DUALITY THEOREMLATTICES (MATHEMATICS)MACHINE LEARNINGREAL NUMBERSINFORMATION THEORYCALCULUSBOOLEAN ALGEBRABayesian probability theory is an inference calculus, which originates from a generalization of inclusion on the Boolean lattice of logical assertions to a degree of inclusion represented by a real number...
Theorem 4.3 Tarski duality The functors described above give a dual equivalence between Set and CABA. For each complete Boolean algebra A, the pair A=(A,≤) is a de Vries algebra of a special kind. Such de Vries algebras are called extremally disconnected in [1] since they correspond to...
Theorem 1 Letbe a pointed-coalgebra that is behaviourally equivalent to a finite well-pointed (=minimal & reachable)-coalgebra. Letbe an expressive language for-coalgebras. Our algorithm determines the well-pointed coalgebrausing queries and counter-examples from. ...