locally ringed space

Short definition from Wiktionary

Noun

1. 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 rings (called the structure sheaf) such that the stalk at each point is a local ring.