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 physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)
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—Ana Castillo (b. 1953)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)