PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (198)
Orphanage
Unclass'd
Unproven (498)
Corrections (25)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Very high Entry average rating: No information on entry rating
ringed space (Definition)

A ringed space is a topological space $ X$ together with a sheaf of commutative rings $ O_X$ on $ X$.

Examples.

  1. Let $ X$ be a topological space and let $ O_X$ be the sheaf of continuous functions.
  2. Let $ X$ be a differentiable manifold and let $ O_X$ be the sheaf of differentiable functions.

Bibliography

1
I.R. Shafarevich, Basic Algebraic Geometry, Springer-Verlag, 1977



"ringed space" is owned by Mathprof.
(view preamble)

View style:

Log in to rate this entry.
(view current ratings)

Cross-references: differentiable functions, differentiable manifold, continuous functions, commutative rings, sheaf, topological space
There are 3 references to this entry.

This is version 2 of ringed space, born on 2006-10-06, modified 2006-10-07.
Object id is 8426, canonical name is RingedSpace.
Accessed 663 times total.

Classification:
AMS MSC: 18F20 (Category theory; homological algebra :: Categories and geometry :: Presheaves and sheaves)
Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)