#
nLab
balanced set

### Context

#### Functional analysis

## Overview diagrams

## Basic concepts

## Theorems

## Topics in Functional Analysis

# Contents

## Definition

A subset $B$ of a vector space $V$ over $\mathbb{R}$ or $\mathbb{C}$ is **balanced** if $\lambda x \in B$ whenever $x \in B$ and ${|\lambda|} \le 1$.

## Properties

The intersection of two balanced sets is balanced. The closure of a balanced set is again balanced.

## Examples

Created on June 18, 2018 at 00:38:28.
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