Finite-dimensional categorical complement theorems in strong shape theory and a principle of reversing maps between open subsets of spheres

Peter Mrozik

Compositio Mathematica (1991)

  • Volume: 77, Issue: 2, page 179-197
  • ISSN: 0010-437X

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Mrozik, Peter. "Finite-dimensional categorical complement theorems in strong shape theory and a principle of reversing maps between open subsets of spheres." Compositio Mathematica 77.2 (1991): 179-197. <http://eudml.org/doc/90071>.

@article{Mrozik1991,
author = {Mrozik, Peter},
journal = {Compositio Mathematica},
keywords = {generalized shape complement; embedding; fundamental dimension; connectivity; strong shape; duality theorem},
language = {eng},
number = {2},
pages = {179-197},
publisher = {Kluwer Academic Publishers},
title = {Finite-dimensional categorical complement theorems in strong shape theory and a principle of reversing maps between open subsets of spheres},
url = {http://eudml.org/doc/90071},
volume = {77},
year = {1991},
}

TY - JOUR
AU - Mrozik, Peter
TI - Finite-dimensional categorical complement theorems in strong shape theory and a principle of reversing maps between open subsets of spheres
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 77
IS - 2
SP - 179
EP - 197
LA - eng
KW - generalized shape complement; embedding; fundamental dimension; connectivity; strong shape; duality theorem
UR - http://eudml.org/doc/90071
ER -

References

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  2. 2 A. Calder and H.M. Hastings, Realizing strong shape equivalences, J. Pure Appl. Algebra20 (1981), 129-156. Zbl0457.55004MR601680
  3. 3 F.W. Cathey, Strong shape theory in: Shape theory and Geometric Topology, (ed. S. Mardešiċ, J. Segal), 215-238Lecture Notes in Math. 870, Springer, Berlin -Heidelberg-New York1981. Zbl0473.55011MR643532
  4. 4 J. Dydak and J. Segal, Strong shape theory, Diss. Math.192 (1981), 1-42. Zbl0474.55007MR627528
  5. 5 D.A. Edwards and H.M. Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Math. 542, Springer, Berlin -Heidelberg-New York1976. Zbl0334.55001MR428322
  6. 6 Q. Haxhibeqiri and S. Nowak, Stable shape, Lecture given at the Conference on Geometric Topology and Shape Theory, Dubrovnik1986. 
  7. 7 Y. Kodama and J. Ono, On fine shape theory, Fund. Math.105 (1979), 29-39. Zbl0425.54016MR558127
  8. 8 Yu. T. Lisica, On the exactness of the spectral homotopy group sequence in shape theory, Soviet Math. Dok.18 (1977), 1186-1190. Zbl0398.55012
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  10. 10 S Mardešić and J. Segal, Shape Theory, North-Holland, Amsterdam1982. Zbl0495.55001MR676973
  11. 11 P. Mrozik, Hereditary shape equivalences and complement theorems, Topology Appl.22 (1986), 131-137. Zbl0598.54006MR836320
  12. 12 P. Mrozik, Chapman's category isomorphism for arbitrary ARs, Fund. Math.125 (1985), 195-208. Zbl0592.57013MR813757
  13. 13 P. Mrozik, Finite-dimensional categorical complement theorems in shape theory, Compositio Math.68 (1988), 161-173. Zbl0665.55006MR966578
  14. 14 S. Nowak, On the relationship between shape properties of subcompacta of Sn and homotopy properties of their complements, Fund. Math.128 (1987), 47- 59. Zbl0633.55009MR919289
  15. 15 D. Quillen, Homotopical Algebra, Lecture Notes in Math. 43, Springer, Berlin -Heidelberg-New York1967. Zbl0168.20903MR223432
  16. 16 R.B. Sher, Complement theorems in shape theory, in: Shape Theory and Geometric Topology (ed. S. Mardešić, J. Segal), 150-168, Lecture Notes in Math. 870, Springer, Berlin-Heidelberg-New York1981. Zbl0494.57007MR643529
  17. 17 R.B. Sher, Complement theorems in shape theory II, in: Geometric Topology and Shape Theory (ed. S. Mardešić, J. Segal), 212-220, Lecture Notes in Math. 1283, Springer, Berlin-Heidelberg -New York1987. Zbl0631.55006MR922283
  18. 18 E.H. Spanier, Algebraic Topology, McGraw-Hill, New York1966. Zbl0145.43303MR210112
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  20. 20 G.A. Venema, Embeddings of compacta in the trivial range, Proc. Amer. Math. Soc.55 (1976), 443-448. Zbl0332.57005MR397738

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