In this paper, we introduce the notion of super finitely separating functions which gives a characterization of RB-domains. Then we prove that FS-domains and RB-domains are equivalent in some special cases by the following three claims: a dcpo is an RB-domain if and only if there exists an approximate identity for it consisting of super finitely separating functions; a consistent join-semilatti...

the aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. all values aretaken in a fixed frame $l$. a definition of (strongly) completelydistributive $l$-ordered sets is introduced. the main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $l$-ordereds...

The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame $L$. A definition of (strongly) completelydistributive $L$-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $L$-ordereds...

We study the relationship between l-groups, Bézout domains, and MV -algebras. Our main motivation and starting point has been the Jaffard-Ohm correspondence between Abelian l-groups and Bézout domains ¶ μ 3 ́ Bézout domains with non-zero unit radical ¶ μ 3 ́ Unital l-groups ¶ μ 3 ́ MV -algebras ©© ©© ©© © HHHHHH ——————————– and Mundici’s equivalence between Abelian unital l-groups and MV -algebras...

Disjunctive systems are a representation of L-domains. They use sequents of the form X ` Y , with X nite and Y pairwise disjoint. We show that for any disjunctive system, its elements ordered by inclusion form an L-domain. On the other hand, via the notion of stable neighborhoods, every L-domain can be represented as a disjunctive system. More generally, we have a categorical equivalence betwee...

The category of L-domains was discovered by A. Jung while solving the problem of nding maximal cartesian closed categories of algebraic CPO's and continuous functions. In this note we analyse properties of the lossless powerdo-main construction, that is closed on the algebraic L-domains. The powerdomain is shown to be isomorphic to a collection of subsets of the domain on which the construction...

A generalisation of Scott's information systems \cite{sco82} is presented that captures exactly all L-domains. The global consistency predicate in definition relativised such a way there for each atomic proposition (token) saying which finite sets statements express consistent with the given statement. It shown states generalised form an L-domain, and L-domain can be generated this way, up to i...