[Guido]

Which reminds me, there are some edge cases to consider. What's the local time for UTC=A? And for UTC=C? I guess the rule is to use half-open intervals on the X axis that are open on the right, so that A maps to Q and C maps to R.

This is clearer ;-) using the hyperreal number line: https://en.wikipedia.org/wiki/Hyperreal_number Transitions theoretically happen at A-h and C-h, where h is any infinitesimal > 0 (any hyperreal number strictly greater than 0 and strictly less than any real number). So your intuition is right. You may ask "but what are the local times corresponding to A-h and C-h?". That would just be making trouble for no good reason. There are far too few points on a real number line to display A-h or C-h, so "who cares?" is appropriate for _many_ reasons ;-)