Mathematics: Theory & Applications

Categorical Closure Operators

Authors: Castellini, Gabriele

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About this Textbook

This book presents the general theory of categorical closure operators to­ gether with a number of examples, mostly drawn from topology and alge­ bra, which illustrate the general concepts in several concrete situations. It is aimed mainly at researchers and graduate students in the area of cate­ gorical topology, and to those interested in categorical methods applied to the most common concrete categories. Categorical Closure Operators is self-contained and can be considered as a graduate level textbook for topics courses in algebra, topology or category theory. The reader is expected to have some basic knowledge of algebra, topology and category theory, however, all categorical concepts that are recurrent are included in Chapter 2. Moreover, Chapter 1 contains all the needed results about Galois connections, and Chapter 3 presents the the­ ory of factorization structures for sinks. These factorizations not only are essential for the theory developed in this book, but details about them can­ not be found anywhere else, since all the results about these factorizations are usually treated as the duals of the theory of factorization structures for sources. Here, those hard-to-find details are provided. Throughout the book I have kept the number of assumptions to a min­ imum, even though this implies that different chapters may use different hypotheses. Normally, the hypotheses in use are specified at the beginning of each chapter and they also apply to the exercise set of that chapter.

Reviews

"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

 


Table of contents (17 chapters)

  • Galois Connections

    Castellini, Gabriele

    Pages 3-8

  • Some Categorical Concepts

    Castellini, Gabriele

    Pages 9-24

  • Factorization Structures For Sinks

    Castellini, Gabriele

    Pages 25-40

  • Closure Operators: Definition and Examples

    Castellini, Gabriele

    Pages 41-56

  • Idempotency, Weak Heredity and Factorization Structures

    Castellini, Gabriele

    Pages 57-63

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-8234-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-0-8176-4250-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-1-4612-6504-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Categorical Closure Operators
Authors
Series Title
Mathematics: Theory & Applications
Copyright
2003
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-8234-7
DOI
10.1007/978-0-8176-8234-7
Hardcover ISBN
978-0-8176-4250-1
Softcover ISBN
978-1-4612-6504-7
Edition Number
1
Number of Pages
XII, 300
Topics