Using the result of Exercise X, prove that the forgetful functor $ \mathbf{CRing} \to \mathbf{Set} $ is isomorphic to $ \mathbf{CRing}(\integers[x], - ) $ , as in Example X. The Sierpi'nski space is the two - point topological space $ S $ in which one of the singleton subsets is open but the other is not. Prove that for any topological space $ X $ , there is a canonical bijection between the open subsets of $ X $ and the continuous maps $ X \to S $ .