Lobachevskii Journal of Mathematics

, Volume 32, Issue 4, pp 328–333 | Cite as

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

  • D. K. Musaev
Article
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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 × 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) the Nagata’s theorem about universality of the product Φ n × B(τ) of universal n-dimensional compact Φ n to B(τ) in the space of all strongly metrizable spaces ≤ τ and dimension dimXn.

Keywords and phrases

superparacompact spaces polyhedra Baire space universal compact complex triangulation 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • D. K. Musaev
    • 1
  1. 1.Romanovskii Institute of MathematicsAcademy of Sciences of UzbekistanTashkentUzbekistan

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