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A functional S-dual in a strong shape category

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Bauer F. W.

Fundamenta Mathematicae

1997

tom 154

nr 3

261-274

In the S-category ${\got P}$ (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 $DX, X = (X,n) ∈ {\got P}$, 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).

A strong shape theory with S-duality

100%

Bauer F. W.

Fundamenta Mathematicae

1997

tom 154

nr 1

37-56

If in the classical S-category $\frakP$, 1)$ continuous mappings are replaced by compact-open strong shape (= {coss}) morphisms (cf. §1 or [1], §2), and 2) ∧-products are properly reinterpreted, then an S-duality theorem for arbitrary subsets $X ⊂ S^n$ (rather than for compact polyhedra) holds (Theorem 2.1).

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2 Fundamenta Mathematicae

2 Bauer F. W.

2 1997

Wyniki wyszukiwania

A functional S-dual in a strong shape category

A strong shape theory with S-duality