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...

We are mainly concerned with some special kinds of semicontinuous domains and relationships between them. New concepts of strongly semicontinuous domains, meet semicontinuous domains and semi-FS domains are introduced. It is shown that a dcpo L is strongly semicontinuous if and only if L is semicontinuous and meet semicontinuous. It is proved that semi-FS domains are strongly semicontinuous. So...

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...

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...

Cumene Hydroperoxide (CHP) has been used in the production of Dicumyl Hydroperoxide (DCPO) and phenol. In Taiwan, several severe fire or explosion incidents have occurred due to its thermal instability or reactivity. In this research, the exothermic decomposition of CHP in Cumene was characterized by isothermal microcalorimeter, TAM (thermal activity monitor), because isothermal testing offers ...

A signature gives rise to a language L (Var) by extending with variables x 2 Var and binding constructs x and x, corresponding to least and greatest xed points respectively. The natural denotational models for such languages are bicomplete dcpos as monotone-algebras. We prove that several approximating denotational semantics have the usual compositional semantics as their limit. These results p...