Definition:Hyperplane/Definition 1

Definition

Let $X$ be a vector space.

Let $U$ be a proper subspace of $X$.

$U$ is a hyperplane if and only if:

for all subspaces $Z$ of $X$ containing $U$, we have either $Z = U$ or $Z = X$.

Also see

• Equivalence of Definitions of Hyperplane

• Results about hyperplanes can be found here.

Sources

• 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $21.3$: Linear Functionals and Hyperplanes