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Abstrakty
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).
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
261-274
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-01-25
Twórcy
autor
- Fachbereich Mathematik, Johann-Wolfgang-Goethe Universität, Robert-Mayer Str. 6-10, 60054 Frankfurt a.M., Germany, f.w.bauer@mathematik.uni-frankfurt.d400.de
Bibliografia
- [1] F. W. Bauer, A strong shape theory admitting an S-dual, Topology Appl. 62 (1995), 207-232.
- [2] F. W. Bauer, A strong shape theory with S-duality, Fund. Math. 154 (1997), 37-56.
- [3] F. W. Bauer, Duality in manifolds, Ann. Mat. Pura Appl. (4) 136 (1984), 241-302.
- [4] J. M. Cohen, Stable Homotopy, Lecture Notes in Math. 165, Springer, Heidelberg, 1970.
- [5] J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.
- [6] B. Günther, The use of semisimplicial complexes in strong shape theory, Glas. Mat. 27 (47) (1992), 101-144.
- [7] E. Spanier, Function spaces and duality, Ann. of Math. 70 (1959), 338-378.
- [8] H. Thiemann, Strong shape and fibrations, Glas. Mat. 30 (50) (1995), 135-174.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv154i3p261bwm