  In this paper we prove that for a compact space $X$ inclusion $P_{f}(X)\in
ANR$ holds if and only if $X\in ANR$. Further, it is shown that the functor
$P_{f}$ preserves property of a compact to be $Q$-manifold or a Hilbert cube,
properties of maps fibres to be $ANR$-compact, $Q$-manifold, Hilbert cube (the
finite of Hilbert cube).
