Category:Examples of Balanced Sets

This category contains examples of Balanced Set.

Let $\GF \in \set {\R, \C}$.

Let $X$ be a vector space over $\GF$.

Let $A \subseteq X$.

We say that $A$ is balanced if and only if:

$s A \subseteq A$ for all $s \in \GF$ with $\cmod s \le 1$

where $s A$ is the dilation of $A$ by $s$.