J. Aust. Math. Soc. 83 (2007), no. 1, pp. 55–77.

An Open Mapping theorem for pro-Lie groups

Karl H. Hofmann Sidney A. Morris
Fachbereich Mathematik
Darmstadt University of Technology
Schlossgartenstr. 7
D-64289 Darmstadt
Germany
hofmann@mathematik.tu-darmstadt.de
School of Information Technology and Mathematical Sciences
University of Ballarat
P.O. Box 663
Ballarat Victoria 3353
Australia
s.morris@ballarat.edu.au
Received 4 July 2005; revised 10 April 2006
Communicated by G. Willis

Abstract

A 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.

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2000 Mathematics Subject Classification: primary 22A05, 22E65; secondary 46A30
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2354??? Z'blatt-MATH: pre05231332
indicates author for correspondence

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