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Mathematical theory of domains

Author: Stoltenberg-Hansen, Viggo ; Lindström, Ingrid ; Griffor, Edward R. Series: Cambridge tracts in theoretical computer science ; 22 Publisher: Cambridge University Press (CUP) 2008.Language: EnglishDescription: 349 p. ; 25 cm.ISBN: 9780521064798Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA76.9 .M35 S76 2008
(Browse shelf)
001254808
Available 001254808
Total holds: 0

Includes bibliographical references and index

Digitized

Mathematical Theory of Domains Contents Preface Chapter 0 Preliminaries 0.1 Some Basic Notions of Set Theory 0.2 Ordered Sets 0.3 Some Basic Notions of Category Theory Part l Basic Theory Chapter 1 Fixed Points 1.1 An Example 1.2 a-complete Partial Orders 1.3 Exercises Chapter 2 Complete Partial Orders 2.1 Complete Partial Orders 2.2 Cartesian Products 2.3 Function Spaces 2.4 Further Constructions 2.5 Exercises Chapter 3 Domains 3.1 Domains 3.2 The Representation Theorem 3.3 Cartesian Closure 3.4 Further Constructions 3.5 Exercises Chapter 4 Domain Equations 4.1 Cusl's 4.2 Direct Limits in Cusl 4.3 co-continuous Functors and Fixed Points 4.4 Least Fixed Points 4.5 Subdomains and Projection Pairs 4.6 Domain Equations 4.7 Exercises ix 1 1 4 8 17 19 19 23 25 28 28 34 38 43 49 53 53 58 63 69 70 74 75 78 83 92 97 104 110 Chapter 5 Topology 5.1 Open and Closed Sets 5.2 Continuity 5.3 Topological Constructions 5.4 Separation Axioms 5.5 Compactness 5.6 Exercises Chapter 6 Representation Theory 6.1 Information Systems 6.2 Formal Spaces 6.3 Relation between Representations 6.4 Solution of Domain Equations to Identity 6.5 Exercises Chapter 7 A Universal Domain 7.1 The Universal Domain U 7.2 Finitary Projections and Subdomains 7.3 Exercises Part II Special Topics Chapter 8 Representability in Domains 8.1 Metric and Ultrametric Spaces 8.2 Ultrametric Algebras as Domains 8.3 Total Elements of Domains 8.4 The Continuous Functionals 8.5 Exercises Chapter 9 Basic Recursion Theory 9.1 Partial Recursive Functions 9.2 Some Basic Results 9.3 Fixed Points Chapter 10 Effective Domains 10.1 Numerations of Abstract Structures 10.2 Computable Cusl's 10.3 Effective Domains 10.4 Constructive Subdomains 10.5 The Myhill-Shepherdson Theorem 10.6 The Kreisel-Lacombe-Shoenfield Theorem 10.7 Exercises Chapter 11 Power Domains 11.1 Definition of the Power Domains 11.2 Closure under the Power Domain Constructions 114 115 119 122 126 129 134 136 137 142 149 152 158 162 163 171 177 181 183 183 193 200 210 219 224 224 229 238 244 244 250 259 267 272 275 280 283 284 295 11.3 An Alternative Definition of SFP-objects Chapter 12 Domains as Models of Formal Theories 304 310 References Index of Symbols Index 332 339 342

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