Closure Operators: Definition and Examples

The aim of this chapter is to introduce the current notion of categorical closure operator (which, as customary, will be simply called closure operator), together with some preliminary results and examples. The first attempts at defining a special case of this new notion of closure operator started in the category Top of topological spaces ([G 1 ] and later [DG 1 ]) and subsequently in a concrete category U: A → X ([C 1 ]). However, in what follows we will skip these two preliminary steps and we will present directly the well established definition in an arbitrary category X that appeared in [DG 3 ]. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.