Categorical Closure Operators (eBook, PDF) von Gabriele Castellini

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...

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Verlag: Birkhäuser Boston
Seitenzahl: 300
Erscheinungstermin: 6. Dezember 2012
Englisch
ISBN-13: 9780817682347
Artikelnr.: 44187041

"The book...presents the contemporary theory of categorical closure operators, one of the main branches of categorical topology. The purpose of the theory is to develop a categorical characterization of the classical topological concepts. It provides a tool that allows us to extend these concepts to an arbitrary category so that the results of the theory have many applications in other fields of mathematics, particularly topology, algebra, and discrete mathematics.... The benefit of the book is that, after introducing the reader to the general theory, it presents a number of applications based on quite recent results achieved in this field. Thus the book provides basic literature for those interested in the theory of closure operators and its applications. It is an excellent exposition of a part of modern mathematics." - INTERNATIONALE MATHEMATISCHE NACHRICHTEN "The book under review puts its emphasis on giving a fairly elementary introduction in to the basic categorical theory of closure operators (Part I) and of their use in categorical topology (Part II), paying particular attention to the author's work on notions of connectedness... Each of the 17 section sof the book ends with a list of references for suggested further reading and a set of exercises, many of which ask the reader to verify claims made earlier in the text." ---ZENTRALBLATT MATH