Answer:
Sure. Let $f_1, f_2, \dots, f_n$ be a family of continuous functions on a set $X$. Let $f(x) = \inf_{i=1}^n f_i(x)$. We want to show that $f$ is upper semicontinuous.
For any $x \in X$ and $\epsilon > 0$, we want to show that the set
$$\{ y \in X : f(y) < f(x) + \epsilon \}$$
is open. This set is the same as
$$\{ y \in X : \inf_{i=1}^n f_i(y) < f(x) + \epsilon \}.$$
Since the functions $f_i$ are continuous, for each $i$, the set
$$\{ y \in X : f_i(y) < f(x) + \epsilon \}$$
is open. Therefore, the set $\{ y \in X : f(y) < f(x) + \epsilon \}$ is the union of open sets, and so it is open.
This shows that $f$ is upper semicontinuous.