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 (232)
Orphanage
Unclass'd
Unproven (519)
Corrections (22)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

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

A topological space $ X$ is said to be normal if $ X$ is $ T_1$ (i.e. singletons are closed), and for all disjoint closed sets $ D,F\subseteq X$ there exist disjoint open sets $ U$ and $ V$ such that $ C\subseteq U$ and $ D\subseteq V$ (i.e, $ X$ is also $ T_4$).

Some authors do not require the $ T_1$ axiom as part of this definition.



"normal" is owned by Koro. [ full author list (3) | owner history (2) ]
(view preamble | get metadata)

View style:

See Also: separation axioms, Tychonoff space, Hausdorff, completely normal, Hausdorff space, a connected normal space with more than one point is uncountable

Other names:  normality, normal
Keywords:  topology
Log in to rate this entry.
(view current ratings)

Cross-references: axiom, open sets, closed sets, disjoint, closed, singletons, topological space
There are 7 references to this entry.

This is version 10 of normal, born on 2002-01-22, modified 2007-05-23.
Object id is 1532, canonical name is NormalTopologicalSpace.
Accessed 6901 times total.

Classification:
AMS MSC: 54D15 (General topology :: Fairly general properties :: Higher separation axioms )
Pending Errata and Addenda
None.
[ View all 5 ]
Discussion
Style: Expand: Order:
forum policy
normal vs T4 by drini on 2004-10-06 13:04:20

my vote goes with T4 begine weaker than normal, since that's how I was taught in 2 different topo courses at two different unis

after all, both this entry and separation axioms are by Koro, so he should just choose the one he prefers and fix either entry
 f
G -----> H G
p \ /_ ----- ~ f(G)
 \ / f ker f
 G/ker f 
[ reply | up ]
Interact
post | correct | update request | add derivation | add example | add (any)