Closed Halfspace

Last updated Nov 1, 2022

Let $V$ be an Inner Product Space over $\mathbb{R}$. A Closed Halfspace is a Set of the form $$H = {x : \langle x, a \rangle \geq b}$$ for any $a \in V$ and $b \in \mathbb{R}$.

1. A Closed Halfspace is Closed. TODO - prove this.
2. If $H$ is an Closed Halfspace, then $\text{int} H$ is an Open Halfspace - TODO prove this.
3. The Boundary of a Closed Halfspace is a Hyperplane - TODO prove this.

• Real Numbers
• Closure