Compact spaces and distributive lattices.
The author presents a general construction connecting compact locales and distributive lattices that allows to reduce results about compact locales to distributive lattices. In the paper there are two applications of the reduction: the localic version of Tychonoff's theorem on the compactness of products and the localic version of Steenrod's theorem on the compactness of inverse limits. The feature of these arguments is that they can be formulated both in topos theory and in a predicative theory.
scientific article; zbMATH DE number 1981481
scientific article