Del i serien Mathematics and Its Applications

Categorical Structure of Closure Operators

With Applications to Topology, Algebra and Discrete Mathematics

Häftad, Engelska, 2010

AvD. Dikranjan,Walter Tholen

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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.

Produktinformation

Utgivningsdatum2010-12-04
Mått155 x 235 x 21 mm
Vikt569 g
FormatHäftad
SpråkEngelska
SerieMathematics and Its Applications
Antal sidor358
FörlagSpringer
ISBN9789048146314

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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.