If (fn) is a bounded sequence of continuous functions on 𝐑^p to 𝐑 and if f* is defined on 𝐑 p by

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First, recall that a function $f: u005Cmathbf{R}^p u005Crightarrow u005Cmathbf{R}$ is upper semiu002Dcontinuous

If $\left(f_n\right)$ is a bounded sequence of continuous functions on $\mathbf{R}^p$ to $\mathbf{R}$ and if $f_$ is defined on $\mathbf{R} p$ by $$ f_(x)=\inf \left\{f_n(x): n \in \mathrm{N}\right\}, x \in \mathbf{R}^p, $$ then is it true that $f_$ is upper semi-continuous on $\mathbf{R}^$ ?