A strong-shape theoretical version of a result due to E. Lima
The S-duality or Spanier-Whitehead duality has been adequately transformed and proved in both shape theoretic setting and strong shape theoretic setting. In fact, the shape theoretic version has been proved, prior to the development of shape theory, by \textit{E. L. Lima} [Summa Brasil. Math. 4, 91-147 (1959; Zbl 0102.383)] and later, independently, by \textit{S. Nowak} [Fundam. Math. 128, 47-60 (1987; Zbl 0633.55009)], while the strong shape theoretic version is proved by \textit{Q. Haxhibeqiri} and \textit{S. Nowak} [Duality between stable strong shape morphisms and stable homotopy classes, Glas. Mat., III. Ser. (to appear)], and this theorem has been announced by the same authors in their paper ``Stable strong shape theory'' [ibid. 24(44), 149-160 (1989; Zbl 0682.55007)]. This theorem states that the stable strong shape category of subcompacta of the n-sphere is isomorphic to the stable homotopy category of their complements. The author of the reviewed paper proves this as a consequence of his results obtained in his previous paper ``Duality in manifolds'' [Ann. Mat. Pura Appl. IV. Ser. 136, 241- 302 (1974; Zbl 0564.55001)].
scientific article; zbMATH DE number 4194699
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