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: