Fibrations in the category of absolute neighborhood retracts

• Autorzy: Miyata T.
• Języki publikacji: EN

Abstrakty

EN

The category Top of topological spaces and continuous maps has the structures of a fibration category and a cofibration category in the sense of Baues, where fibration = Hurewicz fibration, cofibration = the usual cofibration, and weak equivalence = homotopy equivalence. Concentrating on fibrations, we consider the problem: given a full subcategory C of Top, is the fibration structure of Top restricted to C a fibration category? In this paper we take the special case where C is the full subcategory ANR of Top whose objects are absolute neighborhood retracts. The main result is that ANR has the structure of a fibration category if fibration = map having a property that is slightly stronger than the usual homotopy lifting property, and weak equivalence = homotopy equivalence.

Słowa kluczowe

EN

ANR; fibration category; strong homotopy lifting property

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 2
• Strony: 145--154
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Miyata T.

• Department of Mathematics and Informatics, Graduate School of Human Development and Environment, Kobe University, Kobe, 657-8501, Japan,

Bibliografia

• [1] H. J. Baues, Algebraic Homotopy, Cambridge Univ. Press, Cambridge, 1989.
• [2] S. Mardesic and J. Segal, Shape Theory, North-Holland, 1982.
• [3] D. G. Quillen, Homotopical Algebra, Lecture Notes in Math. 43, Springer, 1967.
• [4] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.