Quasi-fibration

In algebraic topology, a quasifibration is a generalisation of fibre bundles and fibrations introduced by Albrecht Dold and René Thom. Roughly speaking, it is a continuous map p: E → B having the same behaviour as a fibration regarding the (relative) homotopy groups of E, B and p⁻¹(x). Equivalently, one can define a quasifibration to be a continuous map such that the inclusion of each fibre into its homotopy fibre is a weak equivalence. One of the main applications of quasifibrations lies in proving the Dold-Thom theorem.