Cylinders and ultrametric topology

The local domains of τ^3 are not open sets chosen from an external space. They are ABCD-prefix cylinders: refinement classes of address tails. Two points are close when their generated address data agree for a long initial segment; their first-disagreement depth δ(t,t’) defines the ultrametric

d(t,t’)=2^-δ(t,t’).

Thus locality is earned from prefix agreement. The topology is the topology of address resolution, not a topology imposed on an already spatial object.