Locally ringed space

English

Noun

1. Template:Lb An abstract mathematical object generalizing the relationship between spaces of functions and the germs of those functions at particular points (i.e. a ringed space) where the analogy with the motivating case is particularly strong. Formally, a topological space equipped with a sheaf of local rings (called the structure sheaf).

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Usage notes

Properly, a locally ringed space is a pair $(X,{𝒪}_X)$ where $X$ is the space and $O_X$ is the structure sheaf. By abuse of notation, $X$ alone may also be referred to as a locally ringed space when ${𝒪}_X$ is understood to be present in some context.