A subset S of a vector space X is an absorbing set if for any point x in X then tx lies in S if t ∈ ℝ is small enough and positive. An alternative name is a ‘radial set’, which reflects the notion that the set S will generate all elements of X in the sense that any x ∈ X can be written as x=α‎s for some s ∈ S and some real α‎.