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1997 | 154 | 1 | 37-56

Tytuł artykułu

A strong shape theory with S-duality

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
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).

Twórcy

  • Fachbereich Mathematik, Johann-Wolfgang-Goethe Universität, Robert-Mayer Str. 6-10, 60054 Frankfurt a.M. 11, 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 theoretical version of a result due to E. Lima, Topology Appl. 40 (1991), 17-21.
  • [3] F. W. Bauer, Duality in manifolds, Ann. Mat. Pura Appl. (4) 136 (1984), 241-302.
  • [4] J. M. Boardman, Stable homotopy is not self-dual, Proc. Amer. Math. Soc. 26 (1970), 369-370.
  • [5] O. Hanner, Some theorems on absolute neighborhood retracts, Ark. Mat. 1 (1952), 389-408.
  • [6] Q. Haxhibeqiri and S. Nowak, Duality between stable strong shape morphisms and stable homotopy classes, Glas. Mat., to appear.
  • [7] E. Lima, The Spanier-Whitehead duality in new homotopy categories, Summa Brasil. Math. 4 (1959), 91-148.
  • [8] T. Y. Lin, Duality and Eilenberg-MacLane spectra, Proc. Amer. Math. Soc. 56 (1976), 291-299.
  • [9] H. R. Margolis, Spectra and the Steenrod Algebra, North-Holland Math. Library 29, North-Holland, 1983.
  • [10] E. Spanier, Algebraic Topology, McGraw-Hill, 1966.

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