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Sibirsk. Mat. Zh., 2021, Volume 62, Number 1, Pages 164–172 (Mi smj7546)  

Solution of Ponomarev's problem of condensation onto compact sets

A. V. Osipovab, E. G. Pytkeevab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: Assuming the Continuum Hypothesis (CH), we prove that there exists a perfectly normal compact topological space $Z$ and a countable set $E\subset Z$ such that $Z\setminus E$ does not condense onto any compact set. The space $Z$ enables us to answer in the negative (under CH) the following problem of Ponomarev: Is each perfectly normal compact set an $a$-space? We also prove that the product of $a$-spaces need not be an $a$-space.

Keywords: condensation, $a$-space, perfectly normal compact set

DOI: https://doi.org/10.33048/smzh.2021.62.114

Full text: PDF file (457 kB)
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UDC: 515.122.5
MSC: 35R30
Received: 11.06.2019
Revised: 18.10.2020
Accepted:18.11.2020

Citation: A. V. Osipov, E. G. Pytkeev, “Solution of Ponomarev's problem of condensation onto compact sets”, Sibirsk. Mat. Zh., 62:1 (2021), 164–172

Citation in format AMSBIB
\Bibitem{OsiPyt21}
\by A.~V.~Osipov, E.~G.~Pytkeev
\paper Solution of Ponomarev's problem of condensation onto compact sets
\jour Sibirsk. Mat. Zh.
\yr 2021
\vol 62
\issue 1
\pages 164--172
\mathnet{http://mi.mathnet.ru/smj7546}
\crossref{https://doi.org/10.33048/smzh.2021.62.114}


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