Categorical Closure Operators

This book presents the general theory of categorical closure operatorstogether with examples and applications to the most common categories,such as topological spaces, fuzzy topological spaces, groups, andabelian groups. The main aim of the theory is to develop a categoricalcharacterization of the classical basic concepts in topology via thenewly introduced concept of categorical closure operators. Thispermits many topological ideas to be introduced in a topology-freeenvironment and imported afterwards into a new category, which oftenyields interesting new insights into its structure.The first part of the book deals with the general theory, startingwith basic definitions and gradually moving to more advancedproperties. The second part includes applications to the classicalconcepts of epimorphisms, separation, compactness and connectedness.Every chapter ends with exercises. A comprehensive list of referencesfor the reader who wants to consult original works and a good indexcomplete the book."Categorical Closure Operators" is self-contained and can beconsidered as a graduate level text for topics courses in categorytheory, algebra, and topology. The book appeals mainly to graduatestudents and researchers in category theory and categorical topology,and to those interested in categorical methods applied to the mostcommon concrete categories. The reader is expected to have some basicknowledge of algebra, topology and category theory; however, allrecurrent categorical concepts are included in a preliminary chapter.