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# 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 $\operatorname{dim}X\le n.$

### Article Information

 Title On generalization of the Freudenthal's theorem for compact irreducible standard polyhedric representation for superparacompact complete metrizable spaces Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 1, 58-64 MathSciNet MR2815371 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

D. K. Musaev
Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, Tashkent, Uzbekistan

### Citation Example

D. K. Musaev, On generalization of the Freudenthal's theorem for compact irreducible standard polyhedric representation for superparacompact complete metrizable spaces, Methods Funct. Anal. Topology 17 (2011), no. 1, 58-64.

### BibTex

@article {MFAT549,
AUTHOR = {Musaev, D. K.},
TITLE = {On generalization of the  Freudenthal's theorem for compact irreducible standard polyhedric representation for superparacompact complete metrizable spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {1},
PAGES = {58-64},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=549},
}