Definition
Formally, a ringed space (X, OX) is a topological space X together with a sheaf of rings OX on X. The sheaf OX is called the structure sheaf of X.
A locally ringed space is a ringed space (X, OX) such that all stalks of OX are local rings (i.e. they have unique maximal ideals). Note that it is not required that OX(U) be a local ring for every open set U. In fact, that is almost never going to be the case.
Read more about this topic: Ringed Space
Famous quotes containing the word definition:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)