Convergence structures and applications to functional analysis - Info and Reading Options

"Convergence structures and applications to functional analysis" Table Of Contents:

• 1- Machine generated contents note: 1 Convergence spaces
• 2- 1.1 Prelim inaries
• 3- 1.2 Initial and final convergence structures
• 4- 1.3 Special convergence spaces, modifications
• 5- 1.4 Compactness
• 6- 1.5 The continuous convergence structure
• 7- 1.6 Countability properties and sequences in convergence spaces
• 8- 1.7 Sequential convergence structures
• 9- 1.8 Categorical aspects
• 10- 2 Uniform convergence spaces
• 11- 2.1 Generalities on uniform convergence spaces
• 12- 2.2 Initial and final uniform convergence structures
• 13- 2.3 Complete uniform convergence spaces
• 14- 2.4 The Arzela-Ascoli thedrem
• 15- 2.5 The uniform convergence structure of a convergence group 3 Convergence vector spaces
• 16- 3.1 Convergence groups
• 17- 3.2 Generalities on convergence vector spaces
• 18- 3.3 Initial and final vector space convergence structures
• 19- 3.4 Projective and inductive limits of convergence vector spaces
• 20- 3.5 The locally convex topological modification
• 21- 3.6 Countability axioms for convergence vector spaces
• 22- 3.7 Boundedness
• 23- 3.8 Notes on bornological vector spaces
• 24- 4 Duality
• 25- 4.1 The dual of a convergence vector space
• 26- 4.2 Reflexivity
• 27- 4.3 The dual of a locally convex topological vector space
• 28- 4.4 An application of continuous duality
• 29- 4.5 Notes
• 30- 5 Hahn-Banach extension theorems
• 31- 5.1 General results
• 32- 5.2 Hahn-Banach spaces
• 33- 5.3 Extending to the adherence
• 34- 5.4 Strong Hahn-Banach spaces
• 35- 5.5 An application to partial differential equations
• 36- 5.6 Notes
• 37- 6 The closed graph theorem
• 38- 6.1 Ultracompleteness
• 39- 6.2 The main theorems
• 40- 6.3 An application to web spaces
• 41- 7 The Banach-Steinhaus theorem
• 42- 7.1 Equicontinuous sets
• 43- 7.2 Banach-Steinhaus pairs
• 44- 7.3 The continuity of bilinear mappings
• 45- 8 Duality theory for convergence groups
• 46- 8.1 Reflexivity
• 47- 8.2 Duality for convergence vector spaces
• 48- 8.3 Subgroups and quotient groups
• 49- 8.4 Topological groups
• 50- 8.5 Groups of unimodular continuous functions
• 51- 8.6 c- and co-duality for topological groups.

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