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Bounded set

From Encyclopedia of Mathematics
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A bounded set in a metric space (with metric ) is a set whose diameter

is finite.

A bounded set in a topological vector space (over a field ) is a set which is absorbed by every neighbourhood of zero (i.e. there exists an such that ).

How to Cite This Entry:
Bounded set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bounded_set&oldid=14421
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article