A categorical guide to separation, compactness and perfectness
From the early seventies, there has been quite a number of publications, in particular by the present author, on categorical versions of the topological concepts in the title. Various levels of generality were considered, in particular in the choice of the class of morphisms (the ``closed'' maps) from which these concepts are defined. By developing the theory of separation and compactness from very general classes of morphisms, the author can compare several existing treatments of related concepts, making the paper, in particular, a useful guide indeed. In addition, the generalization allows applications to non-topological contexts, like extensive categories, Diers' algebraic sets and Janelidze's general Galois theory. (Here are a few light (but potentially annoying) mistakes detected by this reviewer. P. 150, line -13: ``\(m\cdot f\)'' should be ``\(f\cdot m\)''; line -7: ``\(\leq n\)'' should be ``\(\leq c_Y(n)\)''. P. 152, line 12: ``\(1_X\)'' should be ``\(1_Y\)''. P. 156, line -2: ``\(p^*_Z(!_Z)\)'' should be ``\(!_Y^*(!_Z)\)'').
scientific article; zbMATH DE number 1317843