Definition:Ringed Space

Definition

A ringed space is a pair $\struct {X, \OO_X}$ where:

$X$ is a topological space

$\OO_X$ is a sheaf of commutative rings with unity on $X$.

Structure Sheaf

Let $\struct {X, \OO_X}$ be a ringed space.

The structure sheaf of $\struct {X, \OO_X}$ is the term $\OO_X$.

Also see

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