Fiber Strong Shape Theory for Topological Spaces

In the paper we construct and develop a fiber strong shape theory for arbitrary spaces over fixed metrizable space \Bo. Our approach is based on the method of Marde\v{s}i\'{c}-Lisica and instead of resolutions, introduced by Marde\v{s}i\'{c}, their fiber preserving analogues are used. The fiber strong shape theory yields the classification of spaces over \Bo which is coarser than the classification of spaces over \Bo induced by fiber homotopy theory, but is finer than the classification of spaces over \Bo given by usual fiber shape theory

Fiber Strong Shape Theory for Topological Spaces

The purpose of this paper is the construction and investigation of fiber strong shape theory for compact metrizable spaces over a fixed base space B0 , using the fiber versions of cotelescop, fibrant space and SSDR-map. In the paper obtained results containing the characterizations of fiber strong shape equivalences, based on the notion of double mapping cylinder over a fixed space B0. Besides, in the paper we construct and develop a fiber strong shape theory for arbitrary spaces over fixed metrizable space B0. Our approach is based on the method of Mardešić-Lisica and instead of resolutions, introduced by Mardešić, their fiber preserving analogues are used. The fiber strong shape theory yields the classification of spaces over B0 which is coarser than the classification of spaces over B0 induced by fiber homotopy theory, but is finer than the classification of spaces over B0 given by usual fiber shape theory