# On generalization of the Freudentals theorem for compact irreducible standard polyhedric representation for superparacompact complete metrizable spaces

In this paper for superparacompact complete metrizable spaces the Freudenthals theorem for compact irreducible standard polyhedric representation is generalized. Furthermore, for superparacompact metric spaces are reinforced: 1 the Moritas 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 Nagatas 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 $dimX\le n.$

Author: D. K. Musaev; D. I. Jumaev

Source: https://archive.org/