Constructive domain theory as a branch of intuitionistic pointfree topology
نویسندگان
چکیده
منابع مشابه
Constructive Domain Theory as a Branch of Intuitionistic Pointfree Topology
In this paper, the notions of information base and of translation between information bases are introduced; they have a very simple intuitive interpretation and can be taken as an alternative approach to domain theory. Technically, they form a category which is equivalent to the category of Scott domains and approximable mappings. All the definitions and most of the results are inspired by the ...
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The rst paper in this thesis presents a machine checked formalisation, in Martin-Löf's type theory, of pointfree topology with applications to domain theory. In the other papers pointfree topology is used in an approach to constructive analysis. The continuum is de ned as a formal space from a base of rational intervals. Then the closed rational interval [a; b] is de ned as a formal space, in t...
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We will present a formalization of pointfree topology in Martin-Löf's type theory. A notion of point will be introduced and we will show that the points of a Scott topology form a Scott domain. This work follows closely the intuitionistic approach to pointfree topology and domain theory, developed mainly by Martin-Löf and Sambin. The important di erence is that the de nitions and proofs are mac...
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This paper deals with the algebra F(L) of real functions of a frame L and its subclasses LSC(L) and USC(L) of, respectively, lower and upper semicontinuous real functions. It is well-known that F(L) is a lattice-ordered ring; this paper presents explicit formulas for its algebraic operations which allow to conclude about their behaviour in LSC(L) and USC(L). As applications, idempotent function...
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Classically, a Tychonoff space is called strongly 0-dimensional if its Stone-Čech compactification is 0-dimensional, and given the familiar relationship between spaces and frames it is then natural to call a completely regular frame strongly 0-dimensional if its compact completely regular coreflection is 0-dimensional (meaning: is generated by its complemented elements). Indeed, it is then seen...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1996
ISSN: 0304-3975
DOI: 10.1016/0304-3975(95)00169-7