 Homotopy extension property

A pair $(X,A)$ has the homotopy extension property when every homotopy on $A$ whose initial map extends to $X$ can itself be extended to a homotopy on $X$.

The Homotopy Extension Property (HEP) is a fundamental concept in algebraic topology, particularly in the context of topological spaces and homotopy theory. It essentially describes a condition under which homotopies defined on a subspace can be extended to the entire space.