Convergence-theoretic characterizations of compactness (Q1862099)

The author characterizes a variety of notions related to compactness in terms of concretely reflective convergence subcategories: topologies, paratopologies, hypotopologies and pseudotopologies. He also gives characterizations of hyperquotient maps (perfect, quasi-perfect, adherent and closed) and quotient maps (quotient, hereditarily quotient, countably bi-quotient, biquotient and almost open) in terms of various degrees of compactness of their fiber relations, and of sundry relaxations of inverse continuity. The results require too much notation to be describe here, but a good introduction to the theory and well arranged preliminaries are given.