Definition:Hyperplane/Definition 2

Definition

Let $X$ be a vector space.

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

$U$ is a hyperplane (in $X$) if and only if $U$ has codimension $1$ in $X$.

Also see

• Equivalence of Definitions of Hyperplane

• Results about hyperplanes can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): hyperplane
• 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $21.3$: Linear Functionals and Hyperplanes