Open subgroups of free topological groups
Volume 226 / 2014
Fundamenta Mathematicae 226 (2014), 17-40
MSC: Primary 22A05; Secondary 55R65, 55Q52.
DOI: 10.4064/fm226-1-2
Abstract
The theory of covering spaces is often used to prove the Nielsen–Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.
