 Homotopy lifting property

A map $p:E\to B$ has the homotopy lifting property with respect to $X$ when every homotopy $X\times I\to B$ whose initial map lifts to $E$ has a lift extending that initial lift.

The Homotopy Lifting Property (HLP) is a fundamental concept in algebraic topology, particularly in the study of fiber bundles and covering spaces. It describes how homotopies (continuous deformations) can be lifted from the base space to a total space in a fibration or covering space situation.