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 (200)
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: High Entry average rating: No information on entry rating
local base (Definition)

Let $x$ be a point in a topological space $X$. A local base around $x$, is a family of neighborhoods such that every neighborhood of $x$ contains a member of the family. A local base is also known as a neighborhood base.



"local base" is owned by yark. [ full author list (2) | owner history (2) ]
(view preamble)

View style:

See Also: first axiom of countability, neighborhood, neighborhood system

Other names:  base of a neighborhood system, neighborhood base, base of a neighbourhood system, neighbourhood base
Log in to rate this entry.
(view current ratings)

Cross-references: contains, neighborhoods, topological space, point
There are 9 references to this entry.

This is version 6 of local base, born on 2002-02-18, modified 2007-03-26.
Object id is 2121, canonical name is LocalBase.
Accessed 4421 times total.

Classification:
AMS MSC: 54-00 (General topology :: General reference works )
Pending Errata and Addenda
None.
[ View all 4 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

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