Une caractérisation des rétractes absolus de voisinage

Robert Cauty

Fundamenta Mathematicae (1994)

  • Volume: 144, Issue: 1, page 11-22
  • ISSN: 0016-2736

Abstract

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We prove that a metric space is an ANR if, and only if, every open subset of X has the homotopy type of a CW-complex.

How to cite

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Cauty, Robert. "Une caractérisation des rétractes absolus de voisinage." Fundamenta Mathematicae 144.1 (1994): 11-22. <http://eudml.org/doc/212011>.

@article{Cauty1994,
abstract = {We prove that a metric space is an ANR if, and only if, every open subset of X has the homotopy type of a CW-complex.},
author = {Cauty, Robert},
journal = {Fundamenta Mathematicae},
keywords = {homotopy type; CW-complex},
language = {fre},
number = {1},
pages = {11-22},
title = {Une caractérisation des rétractes absolus de voisinage},
url = {http://eudml.org/doc/212011},
volume = {144},
year = {1994},
}

TY - JOUR
AU - Cauty, Robert
TI - Une caractérisation des rétractes absolus de voisinage
JO - Fundamenta Mathematicae
PY - 1994
VL - 144
IS - 1
SP - 11
EP - 22
AB - We prove that a metric space is an ANR if, and only if, every open subset of X has the homotopy type of a CW-complex.
LA - fre
KW - homotopy type; CW-complex
UR - http://eudml.org/doc/212011
ER -

References

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  1. [1] C. J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16. Zbl0175.19802
  2. [2] R. Cauty, Convexité topologique et prolongement des fonctions continues, Compositio Math. 27 (1973), 233-271. Zbl0275.54015
  3. [3] T. tom Dieck, K. H. Kamps und D. Puppe, Homotopietheorie, Lecture Notes in Math. 157, Springer, Berlin, 1970. 
  4. [4] C. H. Dowker, Mapping theorems for non-compact spaces, Amer. J. Math. 69 (1947), 200-242. Zbl0037.10101
  5. [5] R. Engelking, General Topology, PWN, Warszawa, 1977. 
  6. [6] R. Geoghegan, Conjecture 6, in: Proc. Internat. Conf. on Geometric Topology, Warszawa, 1978, Presented Problems, PWN, Warszawa, 1980, p. 463. 
  7. [7] R. Geoghegan, Open problems in infinite-dimensional topology, Topology Proc. 4 (1979), 287-338. Zbl0448.57001
  8. [8] J. B. Giever, On the equivalence of two singular homology theories, Ann. of Math. 51 (1950), 178-191. Zbl0035.38801
  9. [9] S. T. Hu, Theory of Retracts, Wayne State University Press, Detroit, 1965. Zbl0145.43003
  10. [10] G. Kozlowski, Images of ANR's, manuscrit non publié. 
  11. [11] A. R. Pears, Dimension Theory of General Spaces, Cambridge University Press, Cambridge, 1975. 
  12. [12] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. 
  13. [13] A. Strøm, Note on cofibrations II, Math. Scand. 22 (1968), 130-142. Zbl0181.26504
  14. [14] J. E. West, Open problems in infinite dimensional topology, in: Open Problems in Topology, J. van Mill and G. M. Reed (eds.), Elsevier, 1990, 524-597. 

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