Definition:Ringed Space

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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