On generalization of the Freudental's theorem for compact irreducible standard polyhedric representation for superparacompact complete metrizable spaces

Abstract

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 $dimX\le n.$