Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics
Author:   D. Dikranjan ,  Walter Tholen
Publisher:   Springer
Volume:   346
ISBN:  

9780792337720


Pages:   358
Publication Date:   31 October 1995
Format:   Hardback
Availability:   In Print   Availability explained
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Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics


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Overview

This study 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. Knowledge of algebra, topology, and the basic notions of category theory is assumed.

Full Product Details

Author:   D. Dikranjan ,  Walter Tholen
Publisher:   Springer
Imprint:   Springer
Volume:   346
Dimensions:   Width: 15.60cm , Height: 2.20cm , Length: 23.40cm
Weight:   1.570kg
ISBN:  

9780792337720


ISBN 10:   0792337727
Pages:   358
Publication Date:   31 October 1995
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

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.- Index of Definitions.- Notation Index.- Tables of Results.

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


' ... 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


... 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


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