Almost all submaximal groups are paracompact and σ-discrete
Volume 156 / 1998
Fundamenta Mathematicae 156 (1998), 241-260
DOI: 10.4064/fm-156-3-241-260
Abstract
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.
