A finite axiom scheme for approach frames

Enriched Stone-type dualities

“…Last but not least, we would like to point out that this is not the first work transporting classical duality results into the realm of metric spaces. An approach version (see [Lowen, 1997]) of the duality between the categories of sober spaces and continuous maps and of spatial frames and homomorphisms is obtained in [Banaschewski et al, 2006] and extensively studied in [Van Olmen, 2005] (see also [Van Olmen and Verwulgen, 2010]). By definition, an approach frame is a frame with some actions of [0, ∞]; keeping in mind the results of Section 2, we can describe approach frames as particular (co)complete metric spaces.…”