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Weighted quasimetrics, in
 Proc. 8th Summer Conference on General Topology and
, 1994
"... In this article we introduce and investigate the concept of a partial quasimetric and some of its applications. We show that many important constructions studied in Matthews’s theory of partial metrics can still be used successfully in this more general setting. In particular we consider the bicomp ..."
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In this article we introduce and investigate the concept of a partial quasimetric and some of its applications. We show that many important constructions studied in Matthews’s theory of partial metrics can still be used successfully in this more general setting. In particular we consider the bicompletion of the quasimetric space that is associated with a partial quasimetric space and study its applications in groups and BCKalgebras. 1
Weightable QuasiMetric Semigroups and Semilattices
, 2000
"... In [Sch00] a bijection has been established, for the case of semilattices, between invariant partial metrics and semivaluations. Semivaluations are a natural generalization of valuations on lattices to the context of semilattices and arise in many di#erent contexts in Quantitative Domain Theory ..."
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In [Sch00] a bijection has been established, for the case of semilattices, between invariant partial metrics and semivaluations. Semivaluations are a natural generalization of valuations on lattices to the context of semilattices and arise in many di#erent contexts in Quantitative Domain Theory ([Sch00]). Examples of well known spaces which are semivaluation spaces are the Baire quasimetric spaces of [Mat95], the complexity spaces of [Sch95] and the interval domain ([EEP97]).
A CONSTRUCTION METHOD FOR PARTIAL METRICS
"... Abstract. We present a general construction that starts from a family of interiorpreserving open coverings of a given subspace and results in a partial metric with respect to which all subspace elements have selfdistance zero. A necessary and sufficient condition is derived for when this partial m ..."
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Abstract. We present a general construction that starts from a family of interiorpreserving open coverings of a given subspace and results in a partial metric with respect to which all subspace elements have selfdistance zero. A necessary and sufficient condition is derived for when this partial metric induces the given topology. The condition is particularly satisfied if the members of each covering are pairwise disjoint. The method is based on Fletcher’s universal construction for transitive quasiuniformities. Important examples of partial metrics in the literature can be obtained in this way. As a consequence of the construction, the set of all points with selfdistance zero is a Gδ. Moreover, this subspace is zerodimensional in its induced topology. 1.
ManyValued Complete Distributivity ∗
, 2006
"... Suppose (Ω, ∗,I) is a commutative, unital quantale. Categories enriched over Ω can be studied as generalized, or manyvalued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain adjunctions, they can be reformulat ..."
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Suppose (Ω, ∗,I) is a commutative, unital quantale. Categories enriched over Ω can be studied as generalized, or manyvalued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain adjunctions, they can be reformulated in the manyvalued setting in terms of categorical postulations. So, it is possible, by aid of categorical machineries, to establish theories of manyvalued complete lattices, manyvalued completely distributive lattices, and so on. This paper presents a systematical investigation of manyvalued complete distributivity, including the topics: (1) subalgebras and quotient algebras of manyvalued completely distributive lattices; (2) categories of (left adjoint) functors; and (3) the relationship between manyvalued complete distributivity and properties of the quantale Ω. The results show that enriched category theory is a very useful tool in the study of manyvalued versions of orderrelated mathematical entities.
and
"... We discuss a number of distance functions encountered in the theory of computation, including metrics, ultrametrics, quasimetrics, generalized ultrametrics, partial metrics, dultrametrics, and generalized metrics. We consider their properties, associated fixedpoint theorems, and some general ap ..."
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We discuss a number of distance functions encountered in the theory of computation, including metrics, ultrametrics, quasimetrics, generalized ultrametrics, partial metrics, dultrametrics, and generalized metrics. We consider their properties, associated fixedpoint theorems, and some general applications they have within the theory of computation. We consider in detail the applications of generalized distance functions in giving a uniform treatment of several important semantics for logic programs, including acceptable programs and natural generalizations of them, and also the supported model and the stable model in the context of locally stratified extended disjunctive logic programs and databases.
On Some Constructions in Quantitative Domain Theory
"... ) Dieter Spreen Theoretische Informatik, Fachbereich Mathematik Universitat Siegen, 57068 Siegen, Germany Email: spreen@informatik.unisiegen.de 1 ..."
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) Dieter Spreen Theoretische Informatik, Fachbereich Mathematik Universitat Siegen, 57068 Siegen, Germany Email: spreen@informatik.unisiegen.de 1