An open mapping theorem for pro-Lie groups

被引：3

作者：

Hofmann, Karl H. ^{[2
]}

Morris, Sidney A. ^{[1
]}

机构：

[1] Univ Ballarat, Sch Informat Technol & Math Sci, Ballarat, Vic 3353, Australia

[2] Tech Univ Darmstadt, D-64289 Darmstadt, Germany

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2007年 / 83卷

关键词：

D O I：

10.1017/S1446788700036387

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：55 / 77

页数：23

共 16 条

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