On generalization of the Freudenthal’s theorem for compact irreducible standard polyhedric representation for superparacompact complete metrizable spaces - Musaev, D. K. (Methods of Functional Analysis and Topology, 2011)
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^∞× B(τ) of Hilbert cube Q^∞ to generalized Baire space B(τ) of the weight τ in the space of all strongly metrizable spaces of weight τ; 2) Nagata’s theorem about universality of the product Φ^n× B(τ) of the universal n-dimensional compact Φ^n to B(τ) in the space of all strongly metrizable spaces τ and dimension dimXn.