Name: categorical closure operators
SKU: 3620208
Price: 1865.00 TWD
Availability: InStock
Author: castellini
ISBN: 9780817642501

Type

Physical Book

Publisher

Springer

Author

castellini

Language

English

Pages

300

ISBN

0817642501

ISBN13

9780817642501

Synopsis "categorical closure operators"

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.