I think when Dana Scott was first doing this kind of “asymmetric topology” in late 1960-s/early 1970-s, in some of his constructions he did focus on the bases which were like rational numbers, and then it’s really similar in spirit...
(And when I started to work with his formalism in mid-1980-s and early 1990-s, I also focused on those bases, because it was easier to think that way, it was less abstract that way...)
I love this! It’s basically Dedekind cuts, right?
It is related in spirit, yes...
I think when Dana Scott was first doing this kind of “asymmetric topology” in late 1960-s/early 1970-s, in some of his constructions he did focus on the bases which were like rational numbers, and then it’s really similar in spirit...
(And when I started to work with his formalism in mid-1980-s and early 1990-s, I also focused on those bases, because it was easier to think that way, it was less abstract that way...)