A ringed space is a pair $(X, \mathcal{O}_ X)$ consisting of a topological space $X$ and a sheaf of rings $\mathcal{O}_ X$ on $X$. A morphism of ringed spaces $(X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y)$ is a pair consisting of a continuous map $f : X \to Y$ and an $f$-map of sheaves of rings $f^\sharp : \mathcal{O}_ Y \to \mathcal{O}_ X$.