I remember distinctly having the same discrete epiphany, and it is indeed incredibly frustrating. But take heart—this way, you get more than two markers with which to color in your map. :)
You could say that it’s the topology that matters, since you could easily give the globe a topology such that every nation is connected.
You could (as with the indiscrete topology), but in this case I think that it makes more sense to think of the topology as fixed before the particular territories. Historically, the latter have proved to be far more variable.
I remember distinctly having the same discrete epiphany, and it is indeed incredibly frustrating. But take heart—this way, you get more than two markers with which to color in your map. :)
If you have good, bad, lawful, and chaotic guys then you have four colors. That’s enough to color a map, right?
If you assume the world has very simple topology, yes.
You also have to assume that each territory is connected, which is what really makes this theorem inapplicable so often.
You could say that it’s the topology that matters, since you could easily give the globe a topology such that every nation is connected.
You could (as with the indiscrete topology), but in this case I think that it makes more sense to think of the topology as fixed before the particular territories. Historically, the latter have proved to be far more variable.