Abstract
This section is devoted to the construction of the strong shape category SSh(Top) of topological spaces and the strong shape functor \(\bar S\):H(Top)→ SSh(Top). Spaces X, Y are replaced by polyhedral coherent expansions X, Y and the strong shape morphisms F : X → Y are given by homotopy classes [f] of coherent mappings f : X → Y. Existence of coherent expansions is a consequence of the fact that strong expansions (hence, also resolutions) are always coherent expansions. Conversely, coherent HPol — expansions are always strong expansions. It is also shown that mappings, which induce strong shape isomorphisms, can be characterized by rather simple conditions (SM1) and (SM2), which strengthen properties (M1) and (M2).
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Bibliographic notes
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© 2000 Springer-Verlag Berlin Heidelberg
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Mardešić, S. (2000). Strong shape. In: Strong Shape and Homology. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13064-3_9
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DOI: https://doi.org/10.1007/978-3-662-13064-3_9
Publisher Name: Springer, Berlin, Heidelberg
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