nLab Serre fibration

Context

Topology

topology

algebraic topology

Examples

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 $i : \Delta^n \hookrightarrow \Delta^n \times I$ that include the standard topological $n$-simplex $\Delta^n \in$ Top as $\Delta^n \times \{0\}$.

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)