Geometrical and Topological Properties of a Subspace Pf(X) of Probability Measures

We prove that for a compact X, the space Pf(X) is an absolute neighbourhood retract if and only if X is an absolute neighbourhood retract. Further, we demonstrate that a functor Pf preserves the property of a compact to be Q-manifold or Hilbert cube, preserves the property for leaves of maps to be absolute neighbourhood retracts in the class of compacts, to be Q-manifold or Hilbert cube (finite sum of Hilbert cubes).

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