Within Martin-Lőf type theory ([4]), G. Sambin initiated the intuitionistic formal topology which includes Scott algebraic domain theory as a special case (unary formal topology)([7]). In [6], he introduced the notions of (algebraic) information base and translation, and proved the equivalence between the category of (algebraic) information bases and the category of (algebraic) Scott domains. I...

We extend the basic results on the theory of the generalized Riemann integral to the setting of bounded or locally nite measures on locally compact second countable Hausdorr spaces. The correspondence between Borel measures on X and continuous valuations on the upper space UX gives rise to a topological embedding between the space of locally nite measures and locally nite continuous valuations,...

The quasi-interpolation operators of Clément and Scott-Zhang type are generalized to the hp-context. New polynomial lifting and inverse estimates are presented as well.

The present paper investigates the relations between fuzzifying topologies and generalized ideals of fuzzy subsets, as well as constructing generalized ideals and fuzzifying topologies by means of fuzzy preorders. Furthermore, a construction of generalized ideals from preideals, and vice versa, is obtained. As a particular consequence of the results in this paper, a construction of fuzzifying t...

In this thesis I will relate standard computability to computability of reals|and related spaces|and link these notions with denotational semantics of computer languages. The framework for the proposed study was worked out in collaboration with Steve Awodey, Lars Birkedal and Dana Scott. The rst section gives a motivation for our setup and indicates how standard computability ts in it. The subs...

We compare how computational effects are modelled in Classical Domain Theory and Topological Domain Theory. Both of these theories provide powerful toolkits for denotational semantics: Classical Domain Theory being introduced by Scott, and well-established and developed since; Topological Domain Theory being a generalization in which topologies more general than the Scott-topology are admitted....

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...

Given a poset P , the set Γ(P ) of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Posd (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P ) ∼= Γ(Q) implies P ∼= Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Posd is not....