An Open Mapping theorem for pro-Lie groups

• Autores: Karl Heinz Hofmann, Sidney A. Morris
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 83, Nº 1, 2007, págs. 79-86
• Idioma: inglés
• DOI: 10.1017/s1446788700036387
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• Resumen

  • 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.