Path connectivity of spheres in the Gromov–Hausdorff class

Abstract

The paper is devoted to geometrical investigation of Gromov–Hausdorff distance on the classes of all metric spaces and of all bounded metric spaces. The main attention is paid to path connectivity questions. The path connected components of the Gromov–Hausdorff class of all metric spaces are described, and the path connectivity of spheres is proved in several particular cases.