Definition:Restriction of Ringed Space to Open Set

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Definition

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

Let $U \subset X$ be an open subset.

Let $\OO_X {\restriction_U}$ denote the restriction of $\OO_X$ to $U$.


The restriction of $\struct {X, \OO_X}$ to $U$ is the pair $\struct {U, \OO_X {\restriction_U} }$.


Also see