Categorical Closure Operators: Theory & Applications) - Couverture souple

Castellini, Gabriele

Couverture souple

ISBN 10 : 1461265045 ISBN 13 : 9781461265047

Editeur : Birkhäuser, 2012

Synopsis

Presents the general theory of categorical closure operators together with examples and applications to the most common categories, e.g., topological spaces, fuzzy topological spaces, groups, and abelian groups. Part I deals with the general theory, starting with basic definitions and gradually moving to more advanced properties. Part II includes applications to the classical concepts of epimorphisms, separation, compactness and connectedness. Every chapter ends with exercises. A comprehensive bibliography and good index complete this self-contained text, which appeals to graduate students and researchers.

A propos du livre

Présentation de l'éditeur

This book presents the general theory of categorical closure operators together with examples and applications to the most common categories, such as topological spaces, fuzzy topological spaces, groups, and abelian groups. The main aim of the theory is to develop a categorical characterization of the classical basic concepts in topology via the newly introduced concept of categorical closure operators. This permits many topological ideas to be introduced in a topology-free environment and imported afterwards into a new category, which often yields interesting new insights into its structure. The first part of the book deals with the general theory, starting with basic definitions and gradually moving to more advanced properties. The second part includes applications to the classical concepts of epimorphisms, separation, compactness and connectedness. Every chapter ends with exercises. A comprehensive list of references for the reader who wants to consult original works and a good index complete the book. "Categorical Closure Operators" is self-contained and can be considered as a graduate level text for topics courses in category theory, algebra, and topology. The book appeals mainly to graduate students and researchers in category theory and categorical topology, and to those interested in categorical methods applied to the most common concrete categories. The reader is expected to have some basic knowledge of algebra, topology and category theory; however, all recurrent categorical concepts are included in a preliminary chapter.

Détails de l'édition

• Éditeur: Birkhäuser
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 1461265045
• ISBN 13: 9781461265047
• Reliure: Broché
• Nombre de pages: 316
• Coordonnées du fabricant: GPSR Kontakt; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Allemagne