Abstract: A sufficient condition for the strict insertion of a continuous func- tion between two comparable upper and lower semicontinuous functions on a normal space is given. Among immediate corollaries are the classical insertion theorems of Michael and Dowker. Our insertion lemma also provides purely topological proofs of some standard results on closed subsets of normal spaces which normally depend upon uniform convergence of series of continuous func- tions. We also establish a Tietze-type extension theorem characterizing closed $G_\delta$-sets in a normal space.

AMS Subject Classification: 54D15; 54D20; 54C30; 54C20.