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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$.



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Cross-references: neighborhood, bounded, topological vector space
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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 MSC: 46A08 (Functional analysis :: Topological linear spaces and related structures :: Barrelled spaces, bornological spaces)
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