A new look at localic interpolation theorems

This paper presents a new treatment of the localic Katětov–Tong interpolation theorem, based on an analysis of special properties of normal frames, which shows that it does not hold in full generality. Besides giving us the conditions under which the localic Katětov–Tong interpolation theorem holds, this approach leads to a especially transparent and succinct proof of it. It is also shown that this pointfree extension of Katětov–Tong theorem still covers the localic versions of Urysohnʹs Lemma and Tietzeʹs Extension Theorem.