On strong homology of compact spaces

The main purpose of this paper is to describe a natural four-term filtration and the associated graded group of the strong homology group H̄m(X;G) of compact Hausdorff spaces X. This result includes the Milnor exact sequence and the universal coefficient formula. It is also shown that H̄m(X;G) = 0, for m < 0. The proofs depend on the fact that the derived limits limp of the homology progroups pro-Hm(X;G) vanish for p ⩾ 2. Therefore, a detailed proof of this fact is also included.