Comparative Studies of Some Topological Properties on Hyperspaces of Convex Bodies and Wasserstein Hyperspace Associated with Riemannian Manifold

Abstract

The topological properties of some Gromov–Hausdorff hyperspaces of convex bodies associated with Riemannian manifold have been investigated, however, the objective of this paper is to provide a comparative studies of some topological properties on hyperspaces of convex bodies and Wasserstein hyperspace associated with Riemannian manifold, where some of these hyperspaces were proved to be AR, ANR, homogeneous, universal and strongly universal.

Keywords

• hyperspace; Convex body; homeomorphism; diffeomorphism; homotopy