Unitary orbits in 1-dimensional NCCW complexes

Let A   be a 1-dimensional NCCW complex. In this paper, it is shown that the usual distance dUdU defined on the approximate unitary equivalence classes (unitary orbits) of self-adjoints in A   is equal to a distance dWdW defined on morphisms from the Cuntz semigroup of C0(0,1]C0(0,1] to Cu(A)Cu(A). In addition, another distance dPdP on approximately unitary equivalence classes related to spectral information of positive elements in the classes is proved to be equal to dUdU and dWdW on simple unital inductive limits of 1-dimensional NCCW complexes.