On regular $\kappa$-bounded spaces admitting only constant continuous mappings into $T_1$ spaces of pseudo-character $\leq \kappa$

Serhii Bardyla; Alexander V. Osipov

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arXiv · 1912.10423

On regular $\kappa$-bounded spaces admitting only constant continuous mappings into $T_1$ spaces of pseudo-character $\leq \kappa$

Serhii Bardyla·Alexander V. Osipov

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Abstract

In this paper 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 pseudo-character $\leq\kappa$, each continuous function $f:R_{\kappa}\rightarrow Y$ is constant. This result resolves two problems posted by Tzannes in Open Problems from Topology Proceedings and extends results of Ciesielski and Wojciechowski and Herrlich.

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BibTeX RIS

Serhii Bardyla, Alexander V. Osipov. 2019-12-22. On regular $\kappa$-bounded spaces admitting only constant continuous mappings into $T_1$ spaces of pseudo-character $\leq \kappa$. https://arxiv.org/abs/1912.10423

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