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Absorbing Set


A subset B of a vector space E is said to be absorbing if for any x in E, there exists a scalar lambda>0 such that

 x in muB for all mu in F with |mu|>=lambda,

where F is the underlying scalar field of E and where the notation muB denotes the set

 muB={mub:b in B}.

Sets which are absorbing are sometimes said to be radical at 0.


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. "Absorbing Set." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AbsorbingSet.html

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