Categorical Structure of Closure Operators

This study provides a comprehensive categorical theory of closure operators, with applications to topological and uniform spaces, groups, R-modules, fields and topological groups, as well as partially ordered sets and graphs. In particular, closure operators are used to give solutions to the epimorphism and co-well-poweredness problem in many concrete categories. The material is illustrated with many examples and exercises, and open problems are formulated which should stimulate further research. Knowledge of algebra, topology, and the basic notions of category theory is assumed.