We denote $C = \left\{ U \in \mathcal{M}_{n,1}(\mathbb{R}) \mid U^\top U = 1 \right\}$. Prove that $C$ is a closed subset of $\mathcal{M}_{n,1}(\mathbb{R})$.
We denote $C = \left\{ U \in \mathcal{M}_{n,1}(\mathbb{R}) \mid U^\top U = 1 \right\}$. Prove that $C$ is a closed subset of $\mathcal{M}_{n,1}(\mathbb{R})$.