Double closed-graph theorem for topological linear spaces

1967 ◽  
Vol 7 (2) ◽  
pp. 287-300 ◽  
Author(s):  
D. A. Raikov
Keyword(s):  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem ◽  
Linear Spaces ◽  
Topological Linear

B(?)-spaces and the closed graph theorem

1964 ◽  
Vol 153 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Taqdir Husain
Keyword(s):  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem

scholarly journals The closed graph theorem without category

1987 ◽  
Vol 36 (2) ◽  
pp. 283-287 ◽  
Author(s):  
Charles Swartz
Keyword(s):  
Baire Category ◽  
Baire Category Theorem ◽  
Normed Spaces ◽  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem ◽  
Category Theorem

We show that a diagonal theorem of P. Antosik can be used to give a proof of the Closed Graph Theorem for normed spaces which does not depend upon the Baire Category Theorem.

scholarly journals An Open Mapping Theorem For Pro-Lie Groups

2007 ◽  
Vol 83 (1) ◽  
pp. 55-78 ◽  
Author(s):  
Karl H. Hofmann ◽  
Sidney A. Morris
Keyword(s):  
Lie Groups ◽  
Projective Limit ◽  
Factor Group ◽  
Continuous Group ◽  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem ◽  
Open Mapping Theorem ◽  
Finite Dimensional ◽  
Group Modulo

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.

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