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Balanced Set


A subset B of a vector space E is said to be balanced if lambdaB subset= B whenever lambda is a scalar satisfying |lambda|<=1. Here, the notation lambdaB denotes the set

 lambdaB={lambdab:b in B}.

Sets which are balanced are sometimes called circled.


See also

Subset

This entry contributed by Christopher Stover

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References

Wong, Y. Introductory Theory of Topological Vector Spaces. New York: Dekker, 1992.

Cite this as:

Stover, Christopher. "Balanced Set." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/BalancedSet.html

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