# 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

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

## Examples

- In a semi normed vector space the unit ball is absorbing.

## Properties

- The finite intersection of absorbing sets is absorbing

## See also

## References

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