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