If you're using a coordinate system, very simple - you'd just make the day/night status relative to the coordinates. On the most simple level, you could just divide the max coordinates by 24, and use that value as an offset of the time. In practice you'd probably want to make it more advanced than that (otherwise someone could see the sun come up, take a step forward, and then see the sun come up again). If you're NOT using a coordinate system then it's going to be more complex - but you could probably utilise something similar by applying a time offset to each area. The real problem with that is that unless you've got a really large world (which is unlikely with just regular areas), it's going to feel a bit strange.
I've always tended to go for a donut shape (it's nice and simple, and the players are unlikely to notice the difference), although I believe some of the people on MUD-DEV may have utilised a proper globe model (Nathan Yospe or Adam Wiggins, perhaps?). The "patch" approach - whereby the game world represents a piece of a world rather than the whole thing - also works reasonably well, and a flat-earth model would also be quite effective (yet simple to implement).
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