We study properties of metric segments in the class all spaces considered up to an isometry, endowed with Gromov--Hausdorff distance. On isometry classes compact spaces, Gromov-Hausdorff distance is a metric. A segment that consists points lying between two given ones. By von Neumann--Bernays--Godel (NBG) axiomatic set theory, proper monster collection, e.g., collection cardinal sets. prove any...