Matter is continuous into other dimensions, and this is why things like the photon/wave duality can work, interaction with other realities.
In our reality, however, our universe is so sparse as to be almost non-existent (density of the universe is something like 1 hydrogen atom for every 5k cubic meters). This has been measured, and means that our universe is flat (Euclidean).
In my mind, in order to connect the density of the universe with the continuity of quantam behavior, than every reality must have the same density, and flow continuously from ours, which would mean that every reality is Euclidean.
This is where it gets fuzzy for me, because it's my understanding that the multiverse is not Euclidean....