In mathematics, a ringed space is, intuitively speaking, a space together with a collection of commutative rings, the elements of which are "functions" on each open set of the space. Ringed spaces appear throughout analysis and are also used to define the schemes of algebraic geometry.
Other articles related to "ringed space, space, spaces":
... manifolds can be formulated using the notion of a ringed space ... The pair (Rn, O) is an example of a locally ringed space it is a topological space equipped with a sheaf whose stalks are each local rings ... manifold (of class Ck) consists of a pair (M, OM) where M is a second countable Hausdorff space, and OM is a sheaf of local R-algebras defined on M, such that the locally ringed space (M, OM ...
... In the abelian category of finite dimensional vector spaces over a field k, two vector spaces are isomorphic if and only if they have the same dimension ... Thus, for a vector space V the class in ... Finally for a bounded complex of finite dimensional vector spaces V*, where is the standard Euler characteristic defined by is often defined for a ring ...
... Given a locally ringed space (X, OX), certain sheaves of modules on X occur in the applications, the OX-modules ... The category of OX-modules over a fixed locally ringed space (X, OX) is an abelian category ...
Famous quotes containing the words space and/or ringed:
“Mere human beings cant afford to be fanatical about anything.... Not even about justice or loyalty. The fanatic for justice ends by murdering a million helpless people to clear a space for his law-courts. If we are to survive on this planet, there must be compromises.”
—Storm Jameson (18911986)
“But such as you and I do not seem old
Like men who live by habit. Every day
I ride with falcon to the rivers edge
Or carry the ringed mail upon my back,
Or court a woman; neither enemy,
Game-bird, nor woman does the same thing twice....”
—William Butler Yeats (18651939)