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Irresolvable topologies on groups

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Abstract

We prove that there exist ZFC models in which every nondiscrete topological Abelian group can be decomposed into countably many dense subsets. This statement is an answer to the question raised by Comfort and van Mill. We also prove that every submaximal left-topological Abelian group is σ-discrete.

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Authors and Affiliations

  1. Kiev University, Kiev

    I. V. Protasov

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  1. I. V. Protasov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1646–1655, December, 1998.

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Protasov, I.V. Irresolvable topologies on groups. Ukr Math J 50, 1879–1887 (1998). https://doi.org/10.1007/BF02514204

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  • DOI: https://doi.org/10.1007/BF02514204

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