Sur les rétractes absolus Pn -valués de dimension finie

• Autorzy: Robert Cauty
• Języki publikacji: FR

Abstrakty

EN

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.

Słowa kluczowe

EN

$P_k$-valued absolute retracts; stratifiable spaces; ANR.

Kategorie tematyczne

• 54E20: Stratifiable spaces, cosmic spaces, etc.
• 54F15: Continua and generalizations
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 158
• Numer: 3
• Strony: 241-248

Daty

wydano

1998

otrzymano

1997-11-12

Twórcy

autor

Robert Cauty

• Universite Paris 6, UFR 920, Boîte courrier 172, 4 place Jussieu, 75252 Paris Cedex 05, France

Bibliografia

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