We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is Π20 source in the Borel hierarchy. Quasi-Polish spaces can be characterized within the framework of Type-2 Theory of Effectivity as precisely the countably based spaces (...) that have an admissible representation with a Polish domain. They can also be characterized domain theoretically as precisely the spaces that are homeomorphic to the subspace of all non-compact elements of an ω-continuous domain. Every countably based locally compact sober space is quasi-Polish, hence every ω-continuous domain is quasi-Polish. A metrizable space is quasi-Polish if and only if it is Polish. We show that the Borel hierarchy on an uncountable quasi-Polish space does not collapse, and that the Hausdorff–Kuratowski theorem generalizes to all quasi-Polish spaces. (shrink)

The Belgian Constitution of 1831 marked a decisive step in the continental evolution from Restoration constitutional monarchy, based on the monarchical principle, towards the establishment of parliamentary constitutional monarchy. At the time, the new balance of power desired by the Belgian revolutionaries was captured by the phrase ‘republican monarchy’. It is remarkable that this concept, despite being so central to the founding fathers’ deliberations, has hardly been commented upon by later historians and public lawyers. This article aims to reconstruct the (...) origin, meaning and uses of this concept in the context of the 1830 revolutionary wave. French revolutionary veteran general Lafayette was responsible for popularizing republican monarchy in the July Revolution, although the term’s origins went back to eighteenth-century debates on the reform of absolute monarchy. Lafayette used it to summarize the institutional demands of the republican movement vis-à-vis king Louis Philippe. Its transnational migration to the Belgian context subsequently entailed a shift in meaning which will be charted through an analysis of the Belgian constituent and public debates. Finally, the reasons for the concept’s sudden disappearance from the political stage will be addressed. (shrink)