The set of semidualizing complexes is a nontrivial metric space

We show that the set of shift-isomorphism classes of semidualizing complexes over a local ring R admits a nontrivial metric. We investigate the interplay between the metric and several algebraic operations. Motivated by the dagger duality isometry, we prove the following: If K,L are homologically bounded below and degreewise finite R-complexes such that is semidualizing, then K is shift-isomorphic to R. In investigating the existence of nontrivial open balls in , we prove that contains elements that are not comparable in the reflexivity ordering if and only if it contains at least three distinct elements.