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

TL;DR

This paper extends Freudenthal's theorem for superparacompact spaces and reinforces key universality theorems for products involving Hilbert cubes and Baire spaces within strongly metrizable spaces.

Contribution

It generalizes Freudenthal's theorem for superparacompact spaces and strengthens universality results of Morita and Nagata theorems in this context.

Findings

Generalized Freudenthal's theorem for superparacompact complete metrizable spaces.

Reinforced Morita's universality theorem for products involving Hilbert cube and Baire space.

Reinforced Nagata's universality theorem for products involving universal n-dimensional compact and Baire space.

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 $dimX\le n.$