Movable morphisms in strong shape category
Shape theory was introduced by K. Borsuk in the late 60s of the last century with the intention to overcome problems with the classification of spaces having bad local properties, for the study of which homotopy theory is not suitable. Later on \textit{S. Mardešić} in [Strong shape and homology. Berlin: Springer (2000; Zbl 0939.55007)] introduced strong shape theory as an intermediate theory between homotopy and shape theory. Although the classification of spaces induced by isomorphisms in the strong shape category SSh(Top) coincides with the shape type classification, this theory has remained interesting mostly because of the notion of coherent mappings which are essential in its definition. The notion of movability of metrizable compacta was introduced by K. Borsuk for the very first time. In their previous papers [Bull. Pol. Acad. Sci., Math. 64, No. 1, 69--83 (2016; Zbl 1353.55005); Topology Appl. 221, 309--325 (2017; Zbl 1373.55015)] and [\textit{I. Pop}, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 59, No. 1, 25--42 (2013; Zbl 1324.54033)], the present authors have studied various types of movability for shape morphisms. In this work the authors use similar ideas to define movability properties for strong shape morphisms. First they consider a notion of movability of coherent mappings and after proving a series of technical statements they introduce a notion of movability of strong shape morphisms. They obtain some analogous results and give applications on strong shape equivalences between pointed topological spaces.
scientific article; zbMATH DE number 7187648