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.

[edit] Definition

Given a vector space X over a field F a set S is called absorbing if for all $x\in X$ there exists a real number r such that

$\forall \alpha \in \mathbb{F} : \vert \alpha \vert \ge r \Rightarrow x \in \alpha S$

with

$\alpha S := \{ \alpha s \mid s \in S\}$

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