ringed space

English

Noun

ringed space (plural ringed spaces)

1. (sheaf theory, scheme theory) An abstract mathematical object generalizing the relationship between spaces of functions and the germs of those functions at particular points. Formally, a topological space equipped with a sheaf of rings (called the structure sheaf).

Usage notes

Properly, a ringed space is a pair $(X,{\mathcal {O}}_{X})$ 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 ringed space when ${\mathcal {O}}_{X}$ is understood to be present in some context.