Chapter 14: Topology as Invariant of Canonical Denotation

the relevant chapter proved that τ³ is compact, Hausdorff, and totally disconnected — a Stone space (II.D14). But could a different choice of base sets or a different completion strategy produce a different topology on the same underlying set? This chapter proves that the answer is no. The profinite topology is the unique topology making all CRT reduction maps continuous, the space Hausdorff, and the space compact. The ABCD coordinates are determined by the greedy extraction algorithm from Book I’s normal form (I.T04), and the topology is the initial topology with respect to these projections. Since the projections are canonical, so is the topology. There is no “topological creativity” in τ.