locally ringed space

Noun

 * 1)  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).

Usage notes
Properly, a locally 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 locally ringed space when $$\mathcal{O}_X$$ is understood to be present in some context.