> If not that would leave only "a straight line segment can be prolonged indefinitely" as holding, and unlike in Euclidean geometry a straight line segment may intersect itself arbitrarily often.
This one might not hold either, depending on your point of view. If you take the point of view of someone traveling along a line, that can still go on forever.
But if you're measuring the line, portals can easily prevent it from extending indefinitely, by wrapping it around to an earlier part of itself. It would then fail to be the case that, for any distance, there are two points on the line separated by at least that distance.
This one might not hold either, depending on your point of view. If you take the point of view of someone traveling along a line, that can still go on forever.
But if you're measuring the line, portals can easily prevent it from extending indefinitely, by wrapping it around to an earlier part of itself. It would then fail to be the case that, for any distance, there are two points on the line separated by at least that distance.