Abstract
The main goal of the paper is the full proof of a cardinal inequality for a space with points \({G_\delta }\), obtained with the help of a long version of the Menger game. This result, which improves a similar one of Scheepers and Tall, was already established by the authors under the Continuum Hypothesis. The paper is completed by few remarks on a long version of the tightness game.
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Acknowledgments
The authors thank Santi Spadaro for calling their attention to Example 7 and Toshimichi Usuba for his valuable comments. The authors also thank the anonymous referee for the suggestions.
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The research that led to the present paper was done during the visit of the first-named author at the University of Catania and it was partially supported by a grant of the group GNSAGA of INdAM. The first author is also supported by FAPESP, grant 2017/09252-3.
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Aurichi, L.F., Bella, A. A definitive improvement of a game-theoretic bound and the long tightness game. Acta Math. Hungar. 155, 458–465 (2018). https://doi.org/10.1007/s10474-018-0843-6
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DOI: https://doi.org/10.1007/s10474-018-0843-6