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.

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

• bounded set