A new look at localic interpolation theorems
It is shown that, contrarily to what is stated in Li Yong-ming and Wang Guo-jan , the pointfree extension of Katetov-Tong interpolation theorem does not hold in full generality. By presenting a new treatment of it, that leads to a specially transparent and succint proof, based on an analysis of special properties of normal frames, we give the conditions under which it holds. It is also shown that this localic extension of Katetov-Tong theorem still covers the localic versions of Urysohn's lemma and Tietze's extension theorem.
Topology and its Applications