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
Owner confidence rating: Very high Entry average rating: No information on entry rating
bounded set (Definition)

A set in a topological vector space is bounded if it is absorbed by every neighborhood of 0. That is, $ B$ is bounded if for every neighborhood $ U$ of 0, there is a $ \delta > 0$ such that $ \epsilon B \subset U$ for $ 0 \leq \epsilon < \delta$.



"bounded set" is owned by Mathprof.
(view preamble)

View style:

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

Cross-references: neighborhood, bounded, topological vector space
There are 9 references to this entry.

This is version 1 of bounded set, born on 2006-06-11.
Object id is 8004, canonical name is BoundedSet.
Accessed 1363 times total.

Classification:
AMS MSC46A08 (Functional analysis :: Topological linear spaces and related structures :: Barrelled spaces, bornological spaces)

Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

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