Absorbing set

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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.

Definition[edit]

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

with

The notion of the set S being absorbing is different from the notion that S absorbs some other subset T of X since the latter means that there exists some real number r > 0 such that .

Examples[edit]

Properties[edit]

See also[edit]

References[edit]

  • Robertson, A.P.; W.J. Robertson (1964). Topological vector spaces. Cambridge Tracts in Mathematics. 53. Cambridge University Press. p. 4. 
  • Schaefer, Helmut H. (1971). Topological vector spaces. GTM. 3. New York: Springer-Verlag. p. 11. ISBN 0-387-98726-6.