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Fibrations in the Category of Absolute Neighborhood Retracts

Takahisa Miyata (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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...

Finite spaces and the universal bundle of a group

Peter Witbooi (1997)

Commentationes Mathematicae Universitatis Carolinae

We find sufficient conditions for a cotriad of which the objects are locally trivial fibrations, in order that the push-out be a locally trivial fibration. As an application, the universal G -bundle of a finite group G , and the classifying space is modeled by locally finite spaces. In particular, if G is finite, then the universal G -bundle is the limit of an ascending chain of finite spaces. The bundle projection is a covering projection.

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