A functional S-dual in a strong shape category

Friedrich Bauer

Fundamenta Mathematicae (1997)

  • Volume: 154, Issue: 3, page 261-274
  • ISSN: 0016-2736

Abstract

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In the S-category 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 D X , X = ( X , n ) ∈ P , turns out to be of the same weak homotopy type as an appropriately defined functional dual ( S 0 ) X ¯ (Corollary 4.9). Sometimes the functional object X Y ¯ is of the same weak homotopy type as the “real” function space X Y (§5).

How to cite

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Bauer, Friedrich. "A functional S-dual in a strong shape category." Fundamenta Mathematicae 154.3 (1997): 261-274. <http://eudml.org/doc/212237>.

@article{Bauer1997,
abstract = {In the S-category $\{P\}$ (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 $DX, X = (X,n) ∈ \{P\}$, 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).},
author = {Bauer, Friedrich},
journal = {Fundamenta Mathematicae},
keywords = {S-duality; functional S-dual; virtual spaces; weak homotopy type; compact-open strong shape; -duality},
language = {eng},
number = {3},
pages = {261-274},
title = {A functional S-dual in a strong shape category},
url = {http://eudml.org/doc/212237},
volume = {154},
year = {1997},
}

TY - JOUR
AU - Bauer, Friedrich
TI - A functional S-dual in a strong shape category
JO - Fundamenta Mathematicae
PY - 1997
VL - 154
IS - 3
SP - 261
EP - 274
AB - In the S-category ${P}$ (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 $DX, X = (X,n) ∈ {P}$, 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).
LA - eng
KW - S-duality; functional S-dual; virtual spaces; weak homotopy type; compact-open strong shape; -duality
UR - http://eudml.org/doc/212237
ER -

References

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  1. [1] F. W. Bauer, A strong shape theory admitting an S-dual, Topology Appl. 62 (1995), 207-232. Zbl0852.55010
  2. [2] F. W. Bauer, A strong shape theory with S-duality, Fund. Math. 154 (1997), 37-56. Zbl0883.55008
  3. [3] F. W. Bauer, Duality in manifolds, Ann. Mat. Pura Appl. (4) 136 (1984), 241-302. Zbl0564.55001
  4. [4] J. M. Cohen, Stable Homotopy, Lecture Notes in Math. 165, Springer, Heidelberg, 1970. 
  5. [5] J. Dugundji, Topology, Allyn and Bacon, Boston, 1966. 
  6. [6] B. Günther, The use of semisimplicial complexes in strong shape theory, Glas. Mat. 27 (47) (1992), 101-144. Zbl0781.55006
  7. [7] E. Spanier, Function spaces and duality, Ann. of Math. 70 (1959), 338-378. Zbl0090.12905
  8. [8] H. Thiemann, Strong shape and fibrations, Glas. Mat. 30 (50) (1995), 135-174. Zbl0870.55007

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