ringed space

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).

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