# Basic Facts of Semicontinuous Functions

Desvl at
ContinuityWe are restricting ourself into $\mathbb{R}$ endowed with normal topology. Recall that a function is continuous if and only if for any open set $U \subset \mathbb{R}$, we have\{x:f(x) \in U\}=f^{-1}(U)to be open. One can rewrite this statement using $\varepsilon-\delta$ language. To say a ……