Precompactness of Isometric Conjugacy Classes of Continuous Maps
Keywords:
compact metric space, continuous map, Gromov-Hausdorff spaceAbstract
Let $\mathcal{C}$ be the set of isometric conjugacy classes of continuous maps of compact metric spaces equipped with the quasimetric defined by Alexander Arbieto and Carlos Arnoldo Morales Rojas, [Topological stability from Gromov-Hausdorff viewpoint, Discrete Contin. Dyn. Syst. 37 (2017), no. 7, 35313544]. We prove that a subset of $\mathcal{C}$ is precompact if and only if it is equicontinuous.
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