Received 4 July 2005; revised 10 April 2006
Communicated by G. Willis
Abstract
A proLie group is a projective limit of finite dimensional Lie groups. It is proved that a surjective continuous group homomorphism between connected proLie groups is open. In fact this remains true for almost connected proLie 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 proLie groups in the almost connected context.
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2000 Mathematics Subject Classification:
primary 22A05, 22E65; secondary 46A30

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MathSciNet:
MR2354??? 
Z'blattMATH:
pre05231332 
^{†}indicates author for correspondence 
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