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Topology, Domain Theory and Theoretical Computer Science
, 1997
"... In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from ..."
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Cited by 10 (2 self)
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In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from concerns that semantics generates. Keywords: Domain theory, Scott topology, power domains, untyped lambda calculus Subject Classification: 06B35,06F30,18B30,68N15,68Q55 1 Introduction Topology has proved to be an essential tool for certain aspects of theoretical computer science. Conversely, the problems that arise in the computational setting have provided new and interesting stimuli for topology. These problems also have increased the interaction between topology and related areas of mathematics such as order theory and topological algebra. In this paper, we outline some of these interactions between topology and theoretical computer science, focusing on those aspects that have been mo...
Many Familiar Categories Can Be Interpreted as Categories of Generalized Metric Spaces
, 1999
"... The simple concepts of (general) distance function and homometry (a map that preserves distances up to a calibration) are introduced, and it is shown how some natural distance functions on various mathematical objects lead to concrete embeddings of the following categories into the resulting categor ..."
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Cited by 3 (3 self)
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The simple concepts of (general) distance function and homometry (a map that preserves distances up to a calibration) are introduced, and it is shown how some natural distance functions on various mathematical objects lead to concrete embeddings of the following categories into the resulting category DISTÂ°: quasipseudometric, topological and (quasi)uniform spaces with various kinds of maps; groups and latticeordered abelian groups; rings and modules, particularly fields; sets with reexive relations and relationpreserving maps (particularly directed loopless graphs and quasiordered sets); measured spaces with Radoncontinuous maps; Boolean, Brouwerian and orthomodular lattices; categories with combined objects, for example topological groups, ordered topological spaces, ordered elds, Banach spaces with linear contractions or linear continuous maps and so on.