A functional S-dual in a strong shape category
In the S-category (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 , turns out to be of the same weak homotopy type as an appropriately defined functional dual (Corollary 4.9). Sometimes the functional object is of the same weak homotopy type as the “real” function space (§5).