Strong Homology Groups of Continuous Maps

In this paper, we define coherent morphisms of chain maps and homology groups of morphisms of this type. We construct strong homology groups of continuous maps of compact metric spaces and prove that for each continuous map f : X?→?Y , there exists a long exact homological sequence. Moreover, we show that for each inclusion i : A?→?X of compact metric spaces, there exists an isomorphism $ {{bar{H}}_n}(i)approx {{bar{H}}_n}left( {X,A} right) $ .