Abstract. In this paper we give the solution of a problem of P. S. Alexandroff raised as early as 1959 by determining the Pontryagin character group for most homology and cohomology groups. As a consequence, for arbitrary Abelian discrete groups A and B, the dual group to the discrete group Hom(A,B) is described.
1991 Mathematics Subject Classification. 55N07, 55P55, 54B25.
Key words and phrases. Cylinder and cocylinder of chain maps, adjoint direct and inverse systems, homotopy inverse limits, compact direct limits, strong (co)homology, strong compact (co)homology.