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Topological equivalences of \(\mathbf {CUT}\) and \(\mathbf {CUT(Fin)}\)

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Abstract

In this note, two well-known topological facts regarding cofinite and cocountable-like topologies over uncountable sets are shown to be equivalent either to the Countable Union Theorem or to the Countable Union Theorem for countable families of finite sets.

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References

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  3. Wajch, E.: Has it been published somewhere that it can happen in a model for ZF that, for an uncountable set \(S, {\mathbb{R}}^S\) is metrizable? Question posted at ResearchGate, August 11, 2015 (2015)

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Correspondence to Samuel G. da Silva.

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da Silva, S.G. Topological equivalences of \(\mathbf {CUT}\) and \(\mathbf {CUT(Fin)}\) . Arch. Math. Logic 55, 867–872 (2016). https://doi.org/10.1007/s00153-016-0504-9

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  • DOI: https://doi.org/10.1007/s00153-016-0504-9

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