Strong Shape Invariance of Alexander-Spanier Normal Homology Theory

In the paper [Ba-Be-Mdz], using the Alexander-Spanier cochains based on the normal coverings, the exact homology theory ${\bar{H}}_{\ast }^N(-,-;G)$, the so called Alexander-Spanier homology theory, is defined. In the paper we will use the method of construction of the strong homology theory to show that the homology theory ${\bar{H}}_{\ast }^N(-,-;G)$ is a strong shape invariant.