  In this paper for superparacompact complete metrizable spaces the
Freudenthal's theorem for compact irreducible standard polyhedric
representation is generalized. Furthermore, for superparacompact metric spaces
are reinforced: 1) the Morita's theorem about universality of the product
$Q^\infty\times B(\tau)$ of Hilbert cube $Q^\infty$ to generalized Baire space
$B(\tau)$ of the weight $\tau$ in the space of all strongly metrizable spaces
of weight $\le \tau$; 2) the Nagata's theorem about universality of the product
$\Phi^n\times B(\tau)$ of universal $n$- dimensional compact $\Phi^n$ to
$B(\tau)$ in the space of all strongly metrizable spaces $\le\tau$ and
dimension $dimX\le n.$
