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Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad (Oxford Mathematical Monographs)

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Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad (Oxford Mathematical Monographs)
R. Lowen
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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Book Description

In topology the three basic concepts of metrics, topologies and uniformities have been treated so far as separate entities by means of different methods and terminology. This is the first book to treat all three concepts as a special case of the concept of approach spaces. This theory provides an answer to natural questions in the interplay between topological and metric spaces by introducing a uniquely well suited supercategory of TOP and MET. The book explains the richness of approach structures in great detail; it provides a comprehensive explanation of the categorical set-up, develops the basic theory and provides many examples, displaying links with various areas of mathematics such as approximation theory, probability theory, analysis and hyperspace theory.

Categorical Methods in Computer Science: With Aspects from Topology (Lecture Notes in Computer Science)

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Categorical Methods in Computer Science: With Aspects from Topology (Lecture Notes in Computer Science)
H. Ehrig , H. Herrlich , and H. J. Krewski
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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This volume contains selected papers of the International Workshop on "Categorical Methods in Computer Science - with Aspects from Topology" and of the "6th International Data Type Workshop" held in August/September 1988 in Berlin. The 23 papers of this volume are grouped into three parts: Part 1 includes papers on categorical foundations and fundamental concepts from category theory in computer science. Part 2 presents applications of categorical methods to algebraic specification languages and techniques, data types, data bases, programming, and process specifications. Part 3 comprises papers on categorial aspects from topology which mainly concentrate on special adjoint situations like cartesian closeness, Galois connections, reflections, and coreflections which are of growing interest in categorical topology and computer science.

Axiomatic Domain Theory in Categories of Partial Maps (Distinguished Dissertations in Computer Science)

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Axiomatic Domain Theory in Categories of Partial Maps (Distinguished Dissertations in Computer Science)
Marcelo P. Fiore
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them. This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an axiomatic (i.e. abstract) setting. In particular, the author develops theories of partiality and recursive types and applies them to the study of the metalanguage FPC; for example, enriched categorical models of the FPC are defined. Furthermore, FPC is considered as a programming language with a call-by-value operational semantics and a denotational semantics defined on top of a categorical model. To conclude, for an axiomatisation of absolute non-trivial domain-theoretic models of FPC, operational and denotational semantics are related by means of computational soundness and adequacy results. To make the book reasonably self-contained, the author includes an introduction to enriched category theory.

Topology and Category Theory in Computer Science

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Topology and Category Theory in Computer Science

Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0198537603

Book Description

The Oxford Topology Symposium was held in June 1989. Since techniques from topology and category theory have been used increasingly by theoretical computer scientists in recent years, it was decided to hold a special session at the symposium which would be devoted to the application of these topics in computer science. By holding this session in the context of the topology symposium, the organisers hoped to achieve a cross-fertilization between the communities they brought together - giving one a course of new problems with a more practical flavour, and the other a source of solutions and ideas. The session itself proved successful, attracting a large audience of mathematicians as well as computer scientists. The organizing committee decided to produce two separate proceedings for the conference. All those who had presented papers, plus a very few others, were invited to submit papers for these proceedings of the special session on topology and category theory in computer science.

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