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Doklady Mathematics

, Volume 100, Issue 2, pp 430–432 | Cite as

On the Problem of Condensation onto Compact Spaces

  • A. V. OsipovEmail author
  • E. G. Pytkeev
MATHEMATICS
  • 11 Downloads

Abstract

Assuming the continuum hypothesis CH, it is proved that there exists a perfectly normal compact topological space Z and a countable set \(E \subset Z\) such that \(Z{\backslash }E\) is not condensed onto a compact space. The existence of such a space answers (in CH) negatively to V.I. Ponomarev’s question as to whether every perfectly normal compact space is an \(\alpha \)-space. It is proved that, in the class of ordered compact spaces, the property of being an \(\alpha \)-space is not multiplicative.

Notes

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of SciencesYekaterinburgRussia
  2. 2.Ural Federal UniversityYekaterinburgRussia

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