An Open Mapping Theorem For Pro-Lie Groups
2007 ◽
Vol 83
(1)
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pp. 55-78
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Keyword(s):
AbstractA pro-Lie group is a projective limit of finite dimensional Lie groups. It is proved that a surjective continuous group homomorphism between connected pro-Lie groups is open. In fact this remains true for almost connected pro-Lie groups where a topological group is called almost connected if the factor group modulo the identity component is compact. As consequences we get a Closed Graph Theorem and the validity of the Second Isomorphism Theorem for pro-Lie groups in the almost connected context.
Keyword(s):
1961 ◽
Vol s1-36
(1)
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pp. 108-110
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1964 ◽
Vol 15
(3)
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pp. 509
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1987 ◽
Vol 36
(2)
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pp. 283-287
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Keyword(s):
Keyword(s):
1999 ◽
Vol 233
(1)
◽
pp. 77-85
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1967 ◽
Vol 7
(4)
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pp. 433-454
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