# Katětov–Tong insertion theorem

Let ${\displaystyle X}$ be a normal topological space and let ${\displaystyle g,h\colon X\to \mathbb {R} }$ be functions with g upper semicontinuous, h lower semicontinuous and ${\displaystyle g\leq h}$. There exists a continuous function ${\displaystyle f\colon X\to \mathbb {R} }$ with ${\displaystyle g\leq f\leq h.}$