Convergence structures and applications to functional analysis
By: by R. Beattie and H.-P. Butzmann.
Contributors: Butzmann, H.-P.
Publisher: Kluwer Academic Publishers
Published: 2002
Place of publication: Dordrecht; Boston
Language: eng
Number of pages: 264
Subjects: Functional analysis.; Convergence.
Notes: Includes bibliographical references (p. 247-256) and index.
Table of contents: title: Machine generated contents note: 1 Convergence spaces; title: 1.1 Prelim inaries; title: 1.2 Initial and final convergence structures; title: 1.3 Special convergence spaces, modifications; title: 1.4 Compactness; title: 1.5 The continuous convergence structure; title: 1.6 Countability properties and sequences in convergence spaces; title: 1.7 Sequential convergence structures; title: 1.8 Categorical aspects; title: 2 Uniform convergence spaces; title: 2.1 Generalities on uniform convergence spaces; title: 2.2 Initial and final uniform convergence structures; title: 2.3 Complete uniform convergence spaces; title: 2.4 The Arzela-Ascoli thedrem; title: 2.5 The uniform convergence structure of a convergence group 3 Convergence vector spaces; title: 3.1 Convergence groups; title: 3.2 Generalities on convergence vector spaces; title: 3.3 Initial and final vector space convergence structures; title: 3.4 Projective and inductive limits of convergence vector spaces; title: 3.5 The locally convex topological modification; title: 3.6 Countability axioms for convergence vector spaces; title: 3.7 Boundedness; title: 3.8 Notes on bornological vector spaces; title: 4 Duality; title: 4.1 The dual of a convergence vector space; title: 4.2 Reflexivity; title: 4.3 The dual of a locally convex topological vector space; title: 4.4 An application of continuous duality; title: 4.5 Notes; title: 5 Hahn-Banach extension theorems; title: 5.1 General results; title: 5.2 Hahn-Banach spaces; title: 5.3 Extending to the adherence; title: 5.4 Strong Hahn-Banach spaces; title: 5.5 An application to partial differential equations; title: 5.6 Notes; title: 6 The closed graph theorem; title: 6.1 Ultracompleteness; title: 6.2 The main theorems; title: 6.3 An application to web spaces; title: 7 The Banach-Steinhaus theorem; title: 7.1 Equicontinuous sets; title: 7.2 Banach-Steinhaus pairs; title: 7.3 The continuity of bilinear mappings; title: 8 Duality theory for convergence groups; title: 8.1 Reflexivity; title: 8.2 Duality for convergence vector spaces; title: 8.3 Subgroups and quotient groups; title: 8.4 Topological groups; title: 8.5 Groups of unimodular continuous functions; title: 8.6 c- and co-duality for topological groups.