Let $f:\mathbb{R}^{n}\rightrightarrows \mathbb{R}^{m}$ be a set-valued function defined by \begin{equation*} f\left( x\right) =\left\{ y\in \mathbb{R}^{m}:g\left( x\right) +h\left( x\right) ^{T}y\leq 0\right\} \text{,} \end{equation*} where $g:\mathbb{R}^{n}\rightarrow \mathbb{R}$, $h:\mathbb{R}^{n}\rightarrow \mathbb{R}^{m}$ are continuous functions. How do you show that $f$ is continuous in $\mathbb{R}^{n}\diagdown\left\{ 0\right\} $?