Hurewicz fibration

Summary

A Hurewicz fibration is a continuous map $p \colon E \to B$ that has the homotopy lifting property with respect to all topological spaces. Fibrations behave in homotopy theory like fibre bundles. The fibres over points of a path-connected base are homotopy equivalent, and there is a long exact sequence of homotopy groups. A Serre fibration is the weaker notion that asks for the lifting property only for cubes, or equivalently for CW complexes.