A functional S-dual in a strong shape category

• Autorzy: Friedrich W. Bauer
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

S-duality; functional S-dual; virtual spaces; weak homotopy type; compact-open strong shape

Kategorie tematyczne

• 55M05: Duality
• 55P55: Shape theory
• 54C40: Algebraic properties of function spaces
• 55P25: Spanier-Whitehead duality
• 55N20: Generalized (extraordinary) homology and cohomology theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1997
• Tom: 154
• Numer: 3
• Strony: 261-274

Daty

wydano

1997

otrzymano

1996-01-25

Twórcy

autor

Friedrich W. Bauer

• Fachbereich Mathematik, Johann-Wolfgang-Goethe Universität, Robert-Mayer Str. 6-10, 60054 Frankfurt a.M., Germany

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.