Bounded set
From Encyclopedia of Mathematics
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=39503
Bounded set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bounded_set&oldid=39503
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article