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 $F^{'}$ such that the following diagram commutes: $$ \SelectTips{eu}{} \xymatrix{ & A \ar[d]^{i} \ar[r]^{i_{0}} & A \times I \ar[d]^{F} \ar@/^1.5pc/[dd]^{i \times id_{I}} \\ & X \ar[r]^{f} \ar[dr]^{i_{0}} & Y \\ & & X \times I \ar[u]_{F^{'}} } $$ Here, $i_0=(x,0)$ for all $ x \in X$