#
nLab
absorbing subset

Contents
### Context

#### Functional analysis

## Overview diagrams

## Basic concepts

## Theorems

## Topics in Functional Analysis

# Contents

## Definition

Let $V$ be a vector space over $\mathbb{R}$ or $\mathbb{C}$. A subset $B$ of $V$ is said to be **absorbing** if $\bigcup_{r \gt 0} r B = V$.

## Examples

- The unit ball in a seminormed vector space is absorbing.
- The linear span of absolutely convex set $C$ in a vector space has $C$ as an absorbing set.

Last revised on June 18, 2018 at 00:46:16.
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