  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.
