Quasi-fibration

In algebraic topology, a branch of mathematics, a quasi-fibration, introduced by Albrecht Dold and René Thom, is a continuous map of topological spaces formula_1 such that the fibers formula_2 are homotopy equivalent to the homotopy fiber of "f" via the canonical map. 
Every fibration is a quasi-fibration, but the converse is not true. For instance, the projection of the letter L to its base interval is a quasi-fibration (all fibers are contractible), but not a fibration. 