It doesn't make sense to me because a glass of water is a discrete set. If we only had two molecules you could just interchange them (with a 180 degree rotation), without any fixed points.
The space is continuous even if we can only measure down to the Planck length.
I'm only a mathematician, no physicist. But I think to remember, that the concept of a continuous physical space becomes quite muddled at this scale.
If you don't want to assume continuity, then you get it back by rephrasing your theorems as "within a margin of error equal to the distance between discrete objects".