[PatrickHenry]

All that you have in a single dimension universe is the line itself: static, stationary. Nothing can happen to the line without time passing. And there is no time. Thus the line itself cannot be inverted and a point on the line cannot be swapped with another point.

Your one-dimensional universe could consist of a point which is moving in a line. Then you'd have motion (and I suppose you'd have time as well, unless you rule that out as another dimension). If the point reversed direction and went backwards, along the same line, you'd have a reversal. Still all in one dimension.

[Alamo-Girl]

Thank you both for your replies! I can answer both of you with the same post, so in the interest of economy:

A point moving on a line is an event. Every event occurs "in" time. Time passes as a point moves from here to there.

Were it not for time, events would not occur. That is an unequivocal statement.

Inversion is an event. If there is no time in RWP's single dimension universe, an inversion will not occur.

Time is geometric, a dimension.