Geodesic
Almost all submaximal groups are paracompact and σ-discrete
Fundamenta Mathematicae, Tome 156 (1998) no. 3, pp. 241-260.

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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.
DOI : 10.4064/fm-156-3-241-260
Keywords: submaximality, maximality, paracompactness, topological group, separability, σ-discrete, strongly σ-discrete

O. T. Alas 1 ; I. V. Protasov 1 ; M. G. Tkačenko 1 ; V. V. Tkachuk 1 ; R. G. Wilson 1 ; I. V. Yaschenko 1

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O. T. Alas; I. V. Protasov; M. G. Tkačenko; V. V. Tkachuk; R. G. Wilson; I. V. Yaschenko. Almost all submaximal groups are paracompact and σ-discrete. Fundamenta Mathematicae, Tome 156 (1998) no. 3, pp. 241-260. doi : 10.4064/fm-156-3-241-260. http://geodesic.mathdoc.fr/articles/10.4064/fm-156-3-241-260/

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