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
simplicial approximation (Definition)

Let $ K$ and $ L$ be simplicial complexes and $ f: \vert K\vert \to \vert L\vert$ be a continuous function. A simplicial mapping $ g: \vert K\vert \to \vert L\vert$ which is homotopic to $ f$ is called a simplicial approximation of $ f$.

For example, suppose that $ L$ is the closure of an $ n$-simplex and $ a_0$ is a vertex of $ L$. Let $ f$ be a continuous map of $ \vert K\vert$ to $ \vert L\vert$ where $ K$ is some simplicial complex. Then the map $ g$ that sends all of $ K$ to $ a_0$ is a simplicial approximation of $ f$.



"simplicial approximation" is owned by Mathprof.
(view preamble)

View style:

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

Cross-references: map, vertex, closure, homotopic, simplicial mapping, continuous function, simplicial complexes
There are 2 references to this entry.

This is version 3 of simplicial approximation, born on 2007-04-08, modified 2007-04-08.
Object id is 9166, canonical name is SimplicialApproximation.
Accessed 624 times total.

Classification:
AMS MSC: 55U10 (Algebraic topology :: Applied homological algebra and category theory :: Simplicial sets and complexes)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

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