Minkowski space is continuous if time is continuous, surely? Otherwise, why is the 'axis' of the nullcone the time axis? Where is the discontinuity? Oh, crap, of course, it's in chinglu's brain. And about that metric: if Minkowski space isn't a metric space then it cannot have timelike or spacelike 'objects' defined in it. This must be a contradiction since SR is a working theory.