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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. Alternative terms are radial or absorbent set.
Given a vector space X over the field F of real or complex numbers, a set S is called absorbing if for all there exists a real number r such that
- In a semi normed vector space the unit ball is absorbing.
- The finite intersection of absorbing sets is absorbing