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 (204)
Orphanage
Unclass'd
Unproven (490)
Corrections (6)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Low Entry average rating: No information on entry rating
compactification (Definition)

Let $ X$ be a topological space. A (Hausdorff) compactification of $ X$ is a pair $ (K,h)$ where $ K$ is a Hausdorff topological space and $ h:X\rightarrow K$ is a continuous function such that

$ h$ is often considered to be the inclusion map, so that $ X\subseteq K$ with $ \overline{X}^K=K$.



"compactification" is owned by Evandar.
(view preamble)

View style:

See Also: compact, Alexandrov one-point compactification

Other names:  Hausdorff compactification
Log in to rate this entry.
(view current ratings)

Cross-references: inclusion map, subset, closure, homeomorphism, compact, continuous function, Hausdorff topological space, Hausdorff, topological space
There are 4 references to this entry.

This is version 4 of compactification, born on 2002-02-02, modified 2003-09-04.
Object id is 1654, canonical name is Compactification.
Accessed 3729 times total.

Classification:
AMS MSC: 54D35 (General topology :: Fairly general properties :: Extensions of spaces )
Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

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