Absorbing set
From Biocrawler, the free encyclopedia.
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
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Examples
- In a semi normed vector space the unit ball is absorbing.
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Properties
- the finite intersection of absorbing sets is absorbing
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