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Absorbing set
In functional analysis and related areas of mathematics an absorbing set in a vector space is a set S which can be inflated to include any element of the vector space.
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Definition
Given a vector space X over a field F a set S is called absorbing if for all x there exists a real number r such that
with
Examples
- In a semi normed vector space the unit ball is absorbing.
Properties
- the finite intersection of absorbing sets is absorbing
See also
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details