Une caractérisation des rétractes absolus de voisinage

• Autorzy: Robert Cauty
• Języki publikacji: FR

Abstrakty

FR

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.

Kategorie tematyczne

• 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: 1994
• Tom: 144
• Numer: 1
• Strony: 11-22

Daty

wydano

1994

otrzymano

1992-03-03

poprawiono

1993-04-15

Twórcy

autor

Robert Cauty

• 22, Rue Jouvenet F-75016 Paris, Fu

Bibliografia

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