The Katětov–Tong insertion theorem is a theorem of point-set topology proved independently by Miroslav Katětov and Hing Tong in the 1950s.
The theorem states the following:
Let be a normal topological space and let be functions with g upper semicontinuous, h lower semicontinuous and . There exists a continuous function with
This theorem has a number of applications and is the first of many classical insertion theorems. In particular it implies the Tietze extension theorem and consequently Urysohn's lemma, and so the conclusion of the theorem is equivalent to normality.