Sur les rétractes absolus Pn -valués de dimension finie

Robert Cauty

Fundamenta Mathematicae (1998)

  • Volume: 158, Issue: 3, page 241-248
  • ISSN: 0016-2736


We prove that a k-dimensional hereditarily indecomposable metrisable continuum is not a P k -valued absolute retract. We deduce from this that none of the classical characterizations of ANR (metric) extends to the class of stratifiable spaces.

How to cite


Cauty, Robert. "Sur les rétractes absolus Pn -valués de dimension finie." Fundamenta Mathematicae 158.3 (1998): 241-248. <>.

author = {Cauty, Robert},
journal = {Fundamenta Mathematicae},
keywords = {$P_k$-valued absolute retracts; stratifiable spaces; ANR.},
language = {fre},
number = {3},
pages = {241-248},
title = {Sur les rétractes absolus Pn -valués de dimension finie},
url = {},
volume = {158},
year = {1998},

AU - Cauty, Robert
TI - Sur les rétractes absolus Pn -valués de dimension finie
JO - Fundamenta Mathematicae
PY - 1998
VL - 158
IS - 3
SP - 241
EP - 248
LA - fre
KW - $P_k$-valued absolute retracts; stratifiable spaces; ANR.
UR -
ER -


  1. [1] R. H. Bing, Higher-dimensional hereditarily indecomposable continua, Trans. Amer. Math. Soc. 71 (1951), 267-273. Zbl0043.16901
  2. [2] M. Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478-483. Zbl0113.37705
  3. [3] R. Cauty, Un espace métrique linéaire qui n'est pas un rétracte absolu, Fund. Math. 146 (1994), 85-99. 
  4. [4] R. Cauty, Quelques problèmes sur les groupes contractiles et la théorie des rétractes, Mat. Studii 3 (1994), 111-116. 
  5. [5] W. E. Haveri, Locally contractible spaces that are absolute neighborhood retracts, Proc. Amer. Math. Soc. 40 (1973), 280–284 

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