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  • 1 Universidad del País Vasce — Euskal Herriko Unibertsitatea Departmento de Matemáticas Apdo. 644 48080 Bilbao Spain
  • 2 Uniwersytet im. Adama Mickiewicza Wydział Matematyki i Informatyki ul. Umultowska 87 61-614 Poznań Poland
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Abstract  

A sufficient condition for the strict insertion of a continuous function 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 functions. We also establish a Tietze-type extension theorem characterizing closed G δ-sets in a normal space.