Abstract
For each cardinal \(\kappa\) we construct an infinite \(\kappa\)-bounded (and hence countably compact) regular space \(R_{\kappa}\) such that for any \(T_1\) space \(Y\) of pseudocharacter \(\leq\kappa\), each continuous function \(f : R_{\kappa}\rightarrow Y\) is constant. This result resolves two problems posted by Tzannes [13] and extends results of Ciesielski and Wojciechowski [4] and Herrlich [8].
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Acknowledgements
The authors acknowledge Lyubomyr Zdomskyy for his fruitful comments and suggestions. The work reported here was carried out during the visit of the second named author to the KGRC in Vienna. He wishes to thank his colleagues in Vienna.
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The work of the first author is supported by the Austrian Science Fund FWF (Grant I 3709 N35).
The work of the second author was made in the framework of research conducted at the Ural Mathematical Center.
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Bardyla, S., Osipov, A. On regular \(\kappa\)-bounded spaces admitting only constant continuous mappings into \(T_1\) spaces of pseudocharacter \(\leq \kappa\). Acta Math. Hungar. 163, 323–333 (2021). https://doi.org/10.1007/s10474-020-01082-x
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DOI: https://doi.org/10.1007/s10474-020-01082-x