Ringed Space

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.

Read more about Ringed Space:  Definition, Examples, Morphisms, Tangent Spaces, OX Modules

Other articles related to "ringed space, space, spaces":

Differentiable Manifold - Alternative Definitions - Structure Sheaf - Sheaves of Local Rings
... 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 ...
Grothendieck Group - Examples
... 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 ...
Ringed Space - OX Modules
... 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 ...

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