Strong shape theory of continuous maps

V. Baladze, A. Beridze, R. Tsinaridze

The work is motivated by the papers [Ba1], [Ba2], [Ba7], [Ba11], [Be] and [Be-Tu]. In particular, the strong homology groups of continuous maps were defined and studied in [Be] and [Be-Tu]. 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 [Ba7], [Ma3], the strong shape theory of continuous maps of compact metric spaces, the so-called strong fiber shape theory is constructed. 

Tbilisi Mathematical Journal, Special Issue (7 - 2021), pp. 63-98