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.
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The authors are grateful to the referee for careful reading and valuable remarks.
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Osipov, A.V., Pytkeev, E.G. Solution of Ponomarev’s Problem of Condensation onto Compact Sets. Sib Math J 62, 131–137 (2021). https://doi.org/10.1134/S0037446621010146
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DOI: https://doi.org/10.1134/S0037446621010146