nLab
Serre fibration

Serre fibration \Leftarrow Hurewicz fibration \Rightarrow Dold fibration \Leftarrow shrinkable map

Contents

Definition

A Serre fibration is a continuous map between topological spaces that has the right lifting property with respect to all inclusions of the form i:Δ nΔ n×Ii : \Delta^n \hookrightarrow \Delta^n \times I that include the standard topological nn-simplex Δ n\Delta^n \in Top as Δ n×{0}\Delta^n \times \{0\}.

This condition is a special case of that for a Hurewicz fibration.

The Serre fibrations serve as the abstract fibrations in the standard model structure on topological spaces.

Revised on April 7, 2013 19:04:44 by Urs Schreiber (89.204.130.212)