> Yes: there is an order on the set of values of timescales - > it is a basic property of spacetime models that one can distinguish > past and present, at least locally. Spacetime is a differentiable > 4-dimensional manifold, its coordinate functions are usually two > times differentiable or more. In particular, the set of values of > timescales does indeed have a topology (which is Hausdorff).

Sure - this is a reasonable definition of timescale, but I don't think it is wide enough to include UTC. As I understand it, and everyone will correct me if I'm wrong, UTC is not intended to be directly related to spacetime coordinates at all. UTC is (currently) an aproximation to the direction the earth is facing and is adjusted according to how long it takes the earth to end up facing the same direction again. > All of this is completely independent from the choice of a particular > calendar or of the time units to be used for expressing timescale values. I'd agree with this for TAI (including that it should be the integral of a nice 1-form), but I'm not so sure for UTC. > If you subtract a time from a timescale value, you get another > timescale value. If you mean to say that UTC takes its values in a > different space than TAI then you cannot agree with UTC = TAI - DTAI, > as in the official definition of UTC. And if you say that > UTC - TAI can be discontinuous (as a function of whatever) > with both UTC and TAI continuous then you must have a subtraction that > is not continuous. Strange indeed. Where did I misinterpret your post? Yep - you've picked up my intent correctly. I'm saying that subtraction is a stange operator taking a UTC value and a TAI value and gives you something that's a real number. The reason that I came to this conclusion is because none of the documents I've read say that UTC can be expressed as a real number - they all suggest it is expressed as labelled seconds. (For example, see the way that Rec. 460-4 gives UTC values - I've never seen an official looking document that tries to write UTC as a real.) David.