A Generalization of Herrlich's Question on Almost Reflective and Coreflective Subclasses of Top and Unif

摘要

H. Herrlich asked in Topology Appl. 49 (1993), 251-264, whether there are nontrivial classes of topological spaces that are almost reflective and almost coreflective at the same time. This question was dealt with (in Husek and Tozzi, Appl. Categ. Structures 4 (1996), 57-68) in a more general setting than almost reflective and almost coreflective classes. The present paper investigates a modified question: when a nontrivial generalized reflective class of topological or uniform spaces is equivalent to a generalized coreflective class of spaces.