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A Schreier theorem for free topological groups

Published online by Cambridge University Press:  17 April 2009

Peter Nickolas
Peter Nickolas
Affiliation:
School of Mathematics, University of New South Wales, Kensington, New South Wales.
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Abstract

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M.I.Graev has 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 kw-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 necessary condition for freeness of a subgroup. Finally, a sharpened version of a particular case of the theorem is obtained, and is applied to the preceding example.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 1 , August 1975 , pp. 121 - 127
Copyright
Copyright © Australian Mathematical Society 1975

References

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