Generalized reflective cum coreflective classes in Top and Unif

The Herrlich's problem from [8] whether there are nontrivial classes of topological spaces that are both almost reflective or injective and almost coreflective or projective, is investigated in a more general setting using cone and cocone modifications of the classes used in the problem. We look also at the problem for uniform spaces. Typical results: There is no nontrivial multiprojective and orthogonal class of topological spaces; There is a reflective class of uniform spaces that is almost coreflective in Unif.Work on this paper was initiated while the first author was a C.N.R. visitor of the University of L'Aquila. Partial financial assistence by Charles University Grant 349/1994 is also acknowledged.