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A Schreier theorem for free topological groups

1975
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Bulletin of the Australian Mathematical Society
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M.I.Graevhas shown that subgroups of free topological groups need not be free. Brown and Hardy, however, have proved that any open subgroup of the free topological group on a k -space is again a free topological group: indeed, this is true for any closed subgroup for which a Schreier transversal can be chosen continuously. This note provides a proof of this result more direct than that of Brown and Hardy. An example is also given to show that the condition stated in the theorem is not a

doi:10.1017/s0004972700024308
fatcat:i7d34ccyd5gtff32vfsbj6gdwy