More on locales in which every open sublocale is z-embedded

摘要

The locales which have the feature stated in the title (we shall call them Oz-locales) were introduced by Banaschewski and Gilmour as localic extensions of Blair's Oz-spaces. In this note we give further characterisations of Oz-locales and their generalisations which we shall call weak Oz-locales. These characterisations include ring-theoretic ones which are new even for spaces. Among locales L which satisfy some weaker forms of normality, we characterise those for which beta L is an Oz-locale. (C) 2015 Elsevier B.V. All rights reserved.