Coreflections versus regular epimorphisms in categories of topological spaces (Q1272547)

Cagliari and Mantovani have shown that the only non-trivial proper reflective full subcategory of \textbf{Top}, for which the reflector preserves regular monomorphisms, is the one consisting of indiscrete spaces. In the present paper the author shows that, dually, the only non-trivial proper coreflective subcategory of \textbf{Top} (moreover, of any epireflective subcategory of \textbf{Top} that contains at least one non-indiscrete space), for which the coreflector preserves regular epimorphisms, is the one consisting of discrete spaces. This result solves Problem 6 in [\textit{H. Herrlich} and \textit{M. Hušek}, ibid. 1, No. 1, 1-19 (1993; Zbl 0791.54012)].