A characterization of distributive lattices by tolerance lattices
We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context.
We present a direct constructive proof of full normality for a class of spaces (locales) that includes, among others, all metrizable ones.