Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics - Couverture souple

Dikranjan, D.; Tholen, Walter

Couverture souple

ISBN 10 : 9048146313 ISBN 13 : 9789048146314

Editeur : Springer, 2010

Synopsis

Our motivation for gathering the material for this book over aperiod of seven years has been to unify and simplify ideas wh ich appeared in a sizable number of re- search articles during the past two decades. More specifically, it has been our aim to provide the categorical foundations for extensive work that was published on the epimorphism- and cowellpoweredness problem, predominantly for categories of topological spaces. In doing so we found the categorical not ion of closure operators interesting enough to be studied for its own sake, as it unifies and describes other significant mathematical notions and since it leads to a never-ending stream of ex- amples and applications in all areas of mathematics. These are somewhat arbitrarily restricted to topology, algebra and (a small part of) discrete mathematics in this book, although other areas, such as functional analysis, would provide an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni- versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspects only en passant, in favour of the presentation of new results more closely related to our original intentions. We also needed to refrain from studying topological concepts, such as compactness, in the setting of an arbitrary closure-equipped category, although this topic appears prominently in the published literature involving closure operators.

A propos du livre

Présentation de l'éditeur

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 9048146313
• ISBN 13: 9789048146314
• Reliure: Broché
• Nombre de pages: 376
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Allemagne