We prove that Keimel and Lawson's K-completion Kc of the simple valuation monad Vs defines a Kc∘Vs on each -category K. also characterise Eilenberg-Moore algebras as weakly locally convex K-cones, its algebra morphisms continuous linear maps. In addition, we explicitly describe distributive law over Kc, which allows us to show any (resp., convex, linear) topological cone is K-cone. give an exam...

In this paper, the poset $BX$ of formal balls is studied in fuzzy partial metric space $(X,p,*)$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset $BX$ of formal balls is a dcpo if and only if $(X,p,*)$ is layered complete fuzzy partial metric space.

In this article we show how separately continuous algebraic operations on T0-spaces and the laws that they satisfy, both identities and inequalities, can be extended to the D-completion, that is, the universal monotone convergence space completion. Indeed we show that the operations can be extended to the lattice of closed sets, but in this case it is only the linear identities that admit exten...

Abstract It is often useful to be able deal with locales in terms of presentations their underlying frames, or equivalently, the geometric theories which they classify. Given a presentation for locale, its sublocales can obtained by simply appending additional relations, but case quotient more subtle. We provide simple procedures obtaining open quotients, proper quotients general triquotients f...

Abstract We give two concrete examples of continuous valuations on dcpo’s to separate minimal valuations, point-continuous and valuations: (1) Let ${\mathcal J}$ be the Johnstone’s non-sober dcpo, μ valuation with ( U )=1 for nonempty Scott opens )=0 $U=\emptyset$ . Then, is a that not minimal. (2) Lebesgue measure extends Sorgenfrey line $\mathbb{R}_\ell$ Its restriction open subsets λ. its im...

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 power set of a domain D can be seen as the function space D ! 2 of all functions in the pointwise order. One computational version thereof is the lifted lower powerdomain, which we can think of as the lattice of Scott-closed subsets or, alternatively, as the order dual of the function space D ! 2]. Therefore, logic and the ordinary power set, as well as its information-theoretic version, re...

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...

Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness sharp elements. Being apart is positive formulation being unequal, similar to how inhabitedness nonemptiness. To exemplify sharpness, note that lower real if only it located. first main result for large class dcpos, Bridges-Vita topol...