Fibrations in the Category of Absolute Neighborhood Retracts

• Autorzy: Takahisa Miyata
• 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.

Kategorie tematyczne

• 55P30: Eckmann-Hilton duality
• 55U35: Abstract and axiomatic homotopy theory
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: 55
• Numer: 2
• Strony: 145-154

Daty

wydano

2007

Twórcy

autor

Takahisa Miyata

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

Identyfikatory

DOI

10.4064/ba55-2-5