1. The regular closure and epi-closure have been defined for categories of algebras by Isbell [1966] and for categories of topological spaces by Salbany [1976] and Cagliari and Cicchese [1983]. The modification formula 6.3 was given by Dikranjan and Giuli [1984] in topological contexts and by Dikranjan, Giuli and Tholen [1989] for general categories. Frolík communicated a proof of Theorem 6.5 in the context of subcategories of Top to Dikranjan and Giuli in 1983 (see Dikranjan and Giuli [1983]). A categorical version (but more restrictive than the one given in 6.5) was given by Dikranjan, Giuli and Tholen [1989]. Strong modifications were defined by Dikranjan [1992], and the characterization of weakly hereditary regular closure operators (see 6.8) was given by Clementino [1992], [1993]. The correspondences of 6.10 concerning pointed topological spaces are new.