A Schreier theorem for free topological groups
1975 ◽
Vol 13
(1)
◽
pp. 121-127
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Keyword(s):
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.
1993 ◽
Vol 114
(3)
◽
pp. 439-442
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1971 ◽
Vol 4
(1)
◽
pp. 17-29
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1995 ◽
Vol 51
(2)
◽
pp. 309-335
◽
1986 ◽
Vol 40
(3)
◽
pp. 414-420
◽
Keyword(s):
1969 ◽
Vol 1
(2)
◽
pp. 145-160
◽
1973 ◽
Vol 9
(1)
◽
pp. 83-88
◽
1973 ◽
Vol 16
(2)
◽
pp. 220-227
◽
Keyword(s):
1988 ◽
Vol 44
(2)
◽
pp. 252-258
◽
1970 ◽
Vol 2
(2)
◽
pp. 165-178
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Keyword(s):