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Compact condensations of Hausdorff spaces

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Abstract

We continue to study one of the classic problems in general topology raised by P. S. Alexandrov: when a Hausdorff space X has a continuous bijection (a condensation) onto a compactum? We concentrate on the situation when not only X but also \(X\setminus Y\) can be condensed onto a compactum whenever the cardinality of Y does not exceed certain \(\tau\).

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Acknowledgements

The authors would like to thank the referee for careful reading and valuable comments and suggestions. The work was performed as part of research conducted in the Ural Mathematical Center.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Federal University, 620219, Yekaterinburg, Russia

    V. I. Belugin, A. V. Osipov & E. G. Pytkeev

  2. Ural State University of Economics, 620144, Yekaterinburg, Russia

    A. V. Osipov

Authors
  1. V. I. Belugin
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  2. A. V. Osipov
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  3. E. G. Pytkeev
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Correspondence to A. V. Osipov.

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Belugin, V.I., Osipov, A.V. & Pytkeev, E.G. Compact condensations of Hausdorff spaces. Acta Math. Hungar. 164, 15–27 (2021). https://doi.org/10.1007/s10474-021-01131-z

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  • DOI: https://doi.org/10.1007/s10474-021-01131-z

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