Bigger diagrams for solenoids, more automorphisms, colimits

Bigger diagrams make visible more automorphisms: more precisely, bigger diagrams with the same limit make visible more automorphisms of the same object. In the case of the 2-solenoid, this means that we will find a copy of the 2-adic rational numbers [1] Q2 acting on the 2-solenoid, rather than merely the 2-adic integers Z2. This is a big change in the sense that Q2 is non-compact, while Z2 is compact. We had already seen that as a R× Z2 -space 2-solenoid ≈ (R× Z2)/Z where Z is the diagonally imbedded copy of Z. Having found a larger group of automorphisms, we will find that 2-solenoid ≈ (R×Q2)/Z[1/2]