CatGloss

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 $X \to S$ .

This site is open source. Improve this page.