Vector space/Linear subspace/Closed/Definition

Linear subspace

Let ${}K$ be a field, and let ${}V$ be a ${}K$-vector space. A subset ${}U\subseteq V$ is called a linear subspace if the following properties hold.

1. ${}0\in U$.
2. If ${}u,v\in U$, then also ${}u+v\in U$.
3. If ${}u\in U$ and ${}s\in K$, then also ${}su\in U$ holds.