Categorical Closure Operators
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Beschreibung
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.
Castellini has worked in the area of categorical closure operators for over 15 years Combines theory with practice Includes many helpful examples to illustrate the concepts discussed Provides exercises for those interested in self-study Includes applications to classical concepts
Autor*in
Gabriele Castellini
Themen in »Categorical Closure Operators«
Abelian group Boundary value problem Category theory algebra terminal object topology partial differential equations
Stimmen zu »Categorical Closure Operators«
"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
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