Abstract
We prove that if X is a regular space with no uncountable free sequences, then the tightness of its \(G_\delta \) topology is at most the continuum and if X is, in addition, assumed to be Lindelöf then its \(G_\delta \) topology contains no free sequences of length larger then the continuum. We also show that, surprisingly, the higher cardinal generalization of our theorem does not hold, by constructing a regular space with no free sequences of length larger than \(\omega _1\), but whose \(G_\delta \) topology can have arbitrarily large tightness.
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09 March 2021
A Correction to this paper has been published: https://doi.org/10.1007/s00605-021-01543-7
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Acknowledgements
The authors are grateful to INdAM-GNSAGA for partial financial support, to Lajos Soukup for pointing out an error in a previous version of the paper and to the referee for their careful reading of the paper.
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Communicated by S.-D. Friedman.
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Bella, A., Spadaro, S. Upper bounds for the tightness of the \(G_\delta \)-topology. Monatsh Math 195, 183–190 (2021). https://doi.org/10.1007/s00605-020-01495-4
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DOI: https://doi.org/10.1007/s00605-020-01495-4