منابع مشابه
The function ring functors of pointfree topology revisited
This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...
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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...
متن کاملConstructive 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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We generalize a major portion of the classical theory of Cand C embedded subspaces to pointfree topology, where the corresponding notions are frame Cand C -quotients. The central results characterize these quotients and generalize Urysohns Extension Theorem, among others. The proofs require calculations in CL, the archimedean f -ring of frame maps from the topology of the reals into the frame ...
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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: Topology and its Applications
سال: 2004
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(03)00196-2