Strong shape theory of continuous maps
V. Baladze, A. Beridze, R. Tsinaridze
The work is motivated by the papers [Ba_{1}], [Ba_{2}], [Ba_{7}], [Ba_{11}], [Be] and [BeTu]. In particular, the strong homology groups of continuous maps
were defined and studied in [Be] and [BeTu]. To show that the given groups are a homology type functor, it was required to construct a corresponding shape category.
In this paper, we study this very problem. In particular, using the methods developed in [Ba_{7}], [Ma_{3}],
the strong shape theory of continuous maps of compact metric spaces, the socalled strong fiber shape theory is constructed.
Tbilisi Mathematical Journal, Special Issue (7  2021), pp. 6398
