A functional S-dual in a strong shape category

Friedrich W. Bauer¹

¹

Fundamenta Mathematicae, Tome 154 (1997) no. 3, pp. 261-274

Résumé

In the S-category ${\mathfrak P}$ (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual $DX, X = (X,n) ∈ {\mathfrak P}$, turns out to be of the same weak homotopy type as an appropriately defined functional dual $\overline{(S^0)^X}$ (Corollary 4.9). Sometimes the functional object $\overline{X^Y}$ is of the same weak homotopy type as the "real" function space $X^Y$ (§5).

Détail

DOI : 10.4064/fm-154-3-261-274

Keywords: S-duality, functional S-dual, virtual spaces, weak homotopy type, compact-open strong shape