GEOMETRICAL AND TOPOLOGICAL PROPERTIES OF SUBSPACES OF THE SPACE OF PROBABILITY MEASURES THAT ARE MANIFOLDS
Abstract
We study subspaces of the space of probability measures that are finite-dimensional and infinite-dimensional topological manifolds. Studying various properties of the subspaces of the space of probability measures, the following are proved: for any closed subset of the compactum other than itself, there exists a strong deformation retraction , for any infinite and any of its closed subset other than itself, subspace is barycentrically open, for any compact set and for any compact set is compact, for any infinite compact set and any of its closed subset other than , subspace is homeomorphic to the Hilbert space , for any infinite compact set and any of its open subset other than , the subspace is homeomorphic to the Hilbert space , for any compact set and for any the factor space is compact and the projection is a homotopy equivalence, for any compact set and for any the following conditions are equivalent: a) shape is dominated by some compact; b) has a point shape; c)