- Definition
- Examples
- See also
- References
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
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
- In a semi normed vector space the unit ball is absorbing.
See also
- Algebraic interior
- Bounded set (topological vector space)
References
- {{cite book |last=Robertson |first=A.P. |author2= W.J. Robertson |title= Topological vector spaces |series=Cambridge Tracts in Mathematics |volume=53 |year=1964 |publisher= Cambridge University Press | page=4}}
- {{cite book | last = Schaefer | first = Helmut H. | year = 1971 | title = Topological vector spaces | series=GTM | volume=3 | publisher = Springer-Verlag | location = New York | isbn = 0-387-98726-6 | page=11 }}
1 : Functional analysis