I should recall that the **surgenfery topology** on the real numbers is denoted by $\mathbb{R}_l$, and has the set {$[a , b): a,b \in \mathbb{R} $} as it's base. If $X$ is a topological space, an upper semi-continuous real function on $X$ can be interpret as a **continuous function** from $X$ into $\mathbb{R}_l$. The set of all **upper semi-continuous real functions** on $X$ is denoted by $USC(X)$. We could easily see that if we consider $X=\mathbb{R}$ then the set $USC(\mathbb{R})$ is not a ring with pointwise addition and multiplication. because there is $f \in USC(\mathbb{R}) $ so that $-f \notin USC(\mathbb{R}) $. **Indeed it is not a Group**. **Question**.For what condition(s) on $X$, the set $USC(X)$ constructs a ring structure we the pointwise addition and multiplication?