We introduce domain theory in dynamical systems, iterated function systems (fractals) and measure theory. For a discrete dynamical system given by the action of a continuous map f : X ! X on a metric space X, we study the extended dynamical systems (V X; V f), (UX; Uf) and (LX;Lf) where V , U and L are respectively the Vietoris hyperspace, the upper hyperspace and the lower hyperspace functors....

Labelled Markov processes are probabilistic versions of labelled transition systems. In general, the state space of a labelled Markov process may be a continuum. In this paper, we study approximation techniques for continuous-state labelled Markov processes. We show that the collection of labelled Markov processes carries a Polish-space structure with a countable basis given by finite-state Mar...

A construction of fully abstract typed models for PCF and PCF+ (i.e., PCF + “parallel conditional function”), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent non-deterministic strategies introduced by the author in the seventies. Although these notions of strategies are old, the definition of the fully abstract models is...

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...

In 1973 William Lawvere published a paper (reprinted as (Lawvere 2002)) where he explained that partial orders and metric spaces are examples of categories enriched in a closed category. Indeed, preorders are categories enriched over the two-element Boolean algebra 2, while (generalized) metric spaces are categories enriched over ([0,∞],+). Lawvere’s idea has been extremely influential in the f...

K. Martin and P. Panangaden [16] have made the interesting observation that in general relativity theory people have been dealing with partial orders and the way-below relation. From the order theoretical structure of models of spacetime which are called hyperbolic they extract the notion of a strongly hyperbolic poset. In Section 2 I will present these notion, although with a different termino...

We provide a domain-theoretic framework for possibility theory by studying possibility measures on the lattice of opens of a topological space. The powerspaces Poss(X) and Poss 0;1] (X) of all such maps extend to functors in the natural way. We may think of possibility measures as continuous valuations by replacing`+' with`_' in their modular law. The functors above send continuous maps to sup-...

PURPOSE To assess the efficacy of latanoprost (L) and travoprost (T) as monotherapy as well as both drugs associated with 0.5% timolol maleate twice a day regarding the daily curve of intraocular pressure (DCPo) with the measurement of intraocular pressure (IOP) at 6 am in bed. METHODS Retrospective study analyzing the daily curve of intraocular pressure of patients treated with L or T with o...

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 extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...