On generalization of the Freudenthal'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 polyhedral representation is ge e alized. Furthermore, for superparacompact metric spaces the following is strengthened: 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) Nagata's theorem about universality of the product $\Phi^n\times B(\tau)$ of the universal $n$-dimensional compact $\Phi^n$ to $B(\tau)$ in the space of all strongly metrizable spaces $\le\tau$ and dimension $\operatorname{dim}X\le n.$