Definition:Ringed Space

Definition
A ringed space is a pair $\left({X, \mathcal O_X}\right)$ where:
 * $X$ is a topological space
 * $\mathcal O_X$ is a sheaf of rings with unity on $X$

Structure Sheaf
Let $\left({X, \mathcal O_X}\right)$ be a ringed space.

The structure sheaf of $\left({X, \mathcal O_X}\right)$ is the term $\mathcal O_X$.

Also see

 * Definition:Category of Ringed Spaces
 * Definition:Locally Ringed Space