scholarly journals The Closed Graph Theorem for Nonlinear Maps

1999 ◽  
Vol 233 (1) ◽  
pp. 77-85 ◽  
Author(s):  
Antonio Tineo
Keyword(s):  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem ◽  
Nonlinear Maps

Closed Graph Theorem for Qr Spaces

2012 ◽  
Vol 14 (2) ◽  
pp. 193
Author(s):  
Lizhong HUANG
Keyword(s):  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem

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 A closed graph theorem for order bounded operators

2015 ◽  
Vol 39 (2) ◽  
pp. 167-178
Author(s):  
Jan Harm van der Walt
Keyword(s):  
Bounded Operators ◽  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph 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.

scholarly journals A quantitative refinement of the closed graph theorem

1974 ◽  
Vol 24 (3) ◽  
pp. 503-506 ◽  
Author(s):  
Vlastimil Pták
Keyword(s):  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem
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