Almost all submaximal groups are paracompact and σ-discrete

Volume 156 / 1998

O. T. Alas, I. V. Protasov, M. G. Tkačenko, V. V. Tkachuk, R. G. Wilson, I. V. Yaschenko Fundamenta Mathematicae 156 (1998), 241-260 DOI: 10.4064/fm-156-3-241-260


We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.


  • O. T. Alas
  • I. V. Protasov
  • M. G. Tkačenko
  • V. V. Tkachuk
  • R. G. Wilson
  • I. V. Yaschenko

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