Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics by Dikran DikranjanCategorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics by Dikran Dikranjan

Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete…

byDikran Dikranjan, Walter Tholen

Paperback | December 4, 2010

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This book provides a comprehensive categorical theory of closure operators, with applications to topological and uniform spaces, groups, R-modules, fields and topological groups, as well as partially ordered sets and graphs. In particular, closure operators are used to give solutions to the epimorphism and co-well-poweredness problem in many concrete categories. The material is illustrated with many examples and exercises, and open problems are formulated which should stimulate further research. Audience: This volume will be of interest to graduate students and professional researchers in many branches of mathematics and theoretical computer science. Knowledge of algebra, topology, and the basic notions of category theory is assumed.
Title:Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete…Format:PaperbackDimensions:373 pagesPublished:December 4, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048146313

ISBN - 13:9789048146314

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Table of Contents

Preface. Introduction. 1. Preliminaries on Subobjects, Images, and Inverse Images. 2. Basic Properties of Closure Operators. 3. Examples of Closure Operators. 4. Operations on Closure Operators. 5. Closure Operators, Functors, Factorization Systems. 6. Regular Closure Operators. 7. Subcategories Defined by Closure Operators. 8. Epimorphisms and Cowellpoweredness. 9. Dense Maps and Pullback Stability. Bibliography. Index of Definitions. Notation Index. Tables of Results.

Editorial Reviews

` ... substantial enrichment of the literature on closure operators. Anybody working in this field should look into it; in the reviewer's opinion such a look will in most cases be rewarded. ... recommended to mathematicians ... best suited for graduate students and research mathematicians.' Mathematical Reviews Clippings 97i