A new look at localic interpolation theorems

Abstract

This paper presents a new treatment of the localic Katetov-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 Katetov-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 Katetov-Tong theorem still covers the localic versions of Urysohn's Lemma and Tietze's Extension Theorem.