# homotopy extension property

Let $X$ be a topological space^{} and $A$ a subspace^{} of $X$. Suppose there is a continuous map^{} $f:X\to Y$ and a homotopy of maps $F:A\times I\to Y$. The inclusion map $i:A\to X$ is said to have the *homotopy extension property* if there exists a continuous map ${F}^{{}^{\prime}}$ such that the following diagram commutes: