Abstract:
In his preprint Strong homology group of continuous map, A. Beridze defined the strong homology groups $\overline{\mathbf{H}}_*(f)$ of continuous map $f:X\to Y$ of compact metric spaces. Our aim is to show that for these groups, there exist the Milnor short exact sequence. Using the obtained result, we prove that there exists a continuous map with trivial Čech homology groups and nontrivial strong homology groups.
