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Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 164–173 | Cite as

Zero-dimensional CDH spaces with a dense completely metrizable subset

  • S. V. MedvedevEmail author
Article
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Abstract

Given a separable metrizable h-homogeneous space X, it is proved that X is a \(\textsf{CDH}\) space with a dense completely metrizable subspace if and only if every countable subset of X is included in a Polish subspace of X. We also show that every such space is \(\omega-\textsf{CDH}\).

Key words and phrases

h-homogeneous space \(\textsf{CDH}\)-space \(\omega-\textsf{CDH}\) space countably controlled space \(\textsf{KR}\)-cover 

Mathematics Subject Classification

primary 54E52 secondary 54E40 

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Notes

Acknowledgement

The author thanks the anonymous referee for helpful suggestions.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.South Ural State UniversityChelyabinskRussia
  2. 2.Krasovskii Institute of Mathematics and MechanicsEkaterinburgRussia

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