Quantitative semantics, topology, and possibility measures
type: Item
instance of: scholarly article
title: Quantitative semantics, topology, and possibility measures
zbMATH Open document ID: 0927.06004
DOI: 10.1016/S0166-8641(97)00223-X
author: Reinhold Heckmann
author: Michael Huth
published in: Topology and its Applications
publication date: 1999-12-13T00:00:00Z
review text: The authors present a new junction between the world of topological spaces and complete lattices. The main objective of this paper is to develop the notion of quantitative predicates in a topological setting that encompasses that of continuous domains, and to provide a dual view of such quantitative predicates as possibility measures on the lattice of opens. Since we may view any complete lattice \(L\) as a topological space in its Scott topology, we obtain another representation of the order dual of the function space \([L^{\text{op}}\to L^{\text{op}}]\); the lattice \(O(L^{\text{op}})\multimap L\). This should open up the possibility of proving new results in the theory of continuous lattices, especially in bi-continuous lattices.
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 06B30
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 06B23
zbMATH DE Number: 1307930
zbMATH Keywords: topological spaces
zbMATH Keywords: complete lattices
zbMATH Keywords: quantitative predicates
zbMATH Keywords: continuous domains
zbMATH Keywords: possibility measures
zbMATH Keywords: order dual
zbMATH Keywords: function space
zbMATH Keywords: continuous lattices
zbMATH Keywords: bi-continuous lattices
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
cites work: A domain equation for bisimulation
cites work: Q4843177
cites work: Generalized metric spaces: Completion, topology, and powerdomains via the Yoneda embedding
cites work: Q4382654
cites work: Programming as a Discipline of Mathematical Nature
cites work: Integration in Real PCF
cites work: Q4385542
cites work: PCF extended with real numbers
cites work: Q3898534
cites work: Q5726943
cites work: Q4222889
cites work: Q4373421
cites work: A Compositional Approach to Performance Modelling
cites work: An axiomatic basis for computer programming
cites work: Q3915037
cites work: Q4222891
cites work: Q3203061
cites work: Note on free algebras over continuous domains
cites work: Q3992568
cites work: Q3969890
cites work: Q4222902
cites work: Q4347854
cites work: Fuzzy sets
description: scientific article; zbMATH DE number 1307930