We define sequential completeness for ⊤-quasi-uniform spaces using Cauchy pair ⊤-sequences. show that implies and ⊤-uniform with countable bases, are equivalent. As an illustration of the applicability concept, we give a fixed point theorem certain contractive self-mappings in space. This result yields, as special case, probabilistic metric spaces.

Syntax: x; y; z : Var (Internal Names or Variables) Q : Nam (External Names) e : Exp (Expressions) e ::= x j (set! x e) j (e e) j (resolve1 x Q e) j (qs-lambda ((y1 z1) (ym zm)) ((x1 Q1) (xk Qk)) (x) e) Semantic Domains: l : Loc (Locations) : Env = Var ! Loc (Environments) : Inh = Var ! Var (Inheritors) ! : Lnk = Var ! Nam (Links) : Sto = Loc ! Val (Stores) c : Cod = Val ! Env ! Sto ! (Val Sto)...

DoSen, K., Rudimentary Kripe models for the intuitionistic propositional calculus, Annals of Pure and Applied Logic 62 (1993) 21-49. It is shown that the intuitionistic propositional calculus is sound and complete with respect to Kripke-style models that are not quasi-ordered. These models, called rudimentary Kripke models, differ from the ordinary intuitionistic Kripke models by making fewer a...

We sharpen the notion of a quasi-uniform space to spaces which carry with them functional means of approximating points, opens and compacts. Assuming nothing but sobriety, the requirement of uniform approximation ensures that such spaces are compact ordered (in the sense of Nachbin). We study uniformly approximated spaces with the means of topology, uniform topology, order theory and locale the...