Definition 3

Let $K$ be a valued division ring and $E$ a left vector space over $K$; we say that a subset $M$ of $E$ is balanced if, for all $x \in M$ and all $\lambda \in K$ such that $|\lambda| \leq 1$, it is true that $\lambda x \in M$ (or in other words if $\lambda M \subset M$ when $|\lambda| \leq 1$).