Finite-dimensional categorial complement theorems in shape theory

Peter Mrozik

Compositio Mathematica (1988)

  • Volume: 68, Issue: 2, page 161-173
  • ISSN: 0010-437X

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Mrozik, Peter. "Finite-dimensional categorial complement theorems in shape theory." Compositio Mathematica 68.2 (1988): 161-173. <http://eudml.org/doc/89933>.

@article{Mrozik1988,
author = {Mrozik, Peter},
journal = {Compositio Mathematica},
keywords = {shape category; Z-sets in the Hilbert cube; Z-set complements; finite- dimensional complement theorems; m-connected ANR; m-admissible compacta; weak complete m-homotopy category; weak proper m-homotopy category; piecewise linear manifold; ILC embedding condition},
language = {eng},
number = {2},
pages = {161-173},
publisher = {Kluwer Academic Publishers},
title = {Finite-dimensional categorial complement theorems in shape theory},
url = {http://eudml.org/doc/89933},
volume = {68},
year = {1988},
}

TY - JOUR
AU - Mrozik, Peter
TI - Finite-dimensional categorial complement theorems in shape theory
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 68
IS - 2
SP - 161
EP - 173
LA - eng
KW - shape category; Z-sets in the Hilbert cube; Z-set complements; finite- dimensional complement theorems; m-connected ANR; m-admissible compacta; weak complete m-homotopy category; weak proper m-homotopy category; piecewise linear manifold; ILC embedding condition
UR - http://eudml.org/doc/89933
ER -

References

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  1. 1 K. Borsuk: Theory of Retracts. Monografie Matematyczne Tom 44, PWNWarszawa (1967). Zbl0153.52905MR216473
  2. 2 T.A. Chapman: On some applications of infinite-dimensional manifolds to the theory of shape. Fund. Math.76 (1972) 181-193. Zbl0262.55016MR320997
  3. 3 T.A. Chapman: Shapes of finite-dimensional compacta, Fund. Math.76 (1972) 261-276. Zbl0222.55019MR320998
  4. 4 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 York (1976). Zbl0334.55001MR428322
  5. 5 S Mardešić and J. Segal: Shape Theory. North Holland, Amsterdam (1982). Zbl0495.55001MR676973
  6. 6 R.E. Mosher and M.C. Tangora: Cohomology Operations and Applications in Homotopy Theory. Harper & Row, New York (1968). Zbl0153.53302MR226634
  7. 7 P. Mrozik: Chapman's category isomorphism for arbitrary ARs. Fund. Math.125 (1985) 195-208. Zbl0592.57013MR813757
  8. 8 R.B. Sher: Complement theorems in shape theory. In: Shape Theory and Geometric Topology S. Mardešić and J. Segal (ed.) Lecture Notes in Math.870, Springer, Berlin-Heidelberg -New York (1981) pp. 150-168. Zbl0494.57007MR643529
  9. 9 E.H. Spanier: Algebraic Topology. McGraw-Hill, New York (1966). Zbl0145.43303MR210112
  10. 10 G. Venema: Embeddings of compacta with shape dimension in the trivial range. Proc. Amer. Math. Soc.55 (1976) 443-448. Zbl0332.57005MR397738
  11. 11 G. Venema: Embeddings in shape theory. In: Shape Theory and Geometric Topology. S. Mardešić and J. Segal (eds.) Lecture Notes in Math.870, Springer, Berlin-Heidelberg -New York (1981) pp. 169-185. Zbl0491.57009MR643530

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