Exercise 26, § 1

On the set $X =\{0,1\}$, consider the topology for which the open sets are $\emptyset ,\{0\}$ and X. Let $A =\{0\}$. Exercise prove that the pair $(X,A)$ has the property of extension of homotopies but that the pair $(X\times X,(X\times A)\cup (A\times X))$ does not possess it.