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

Inhalt
I GENERAL THEORY.- 1 Galois Connections.- 2 Some Categorical Concepts.- 3 Factorization Structures For Sinks.- 4 Closure Operators: Definition and Examples.- 5 Idempotency, Weak Heredity and Factorization Structures.- 6 Additivity, Heredity, Suprema and Infima of Closure Operators.- 7 Additional Descriptions of ? and ? and Subobject Orthogonality.- 8 A Diagram of Galois Connections of Closure Operators.- 9 Regular Closure Operators.- 10 Hereditary Regular Closure Operators.- 11 APPLICATIONS.- 11 Epimorphisms.- 12 Separation.- 13 Compactness.- 14 Connectedness.- 15 Connectedness in Categories with a Terminal Object.- 16 A Link between two Connectedness Notions.- 17 Different Constructions Related.- References.- List of Symbols.