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Book Categories |
| Introduction | ||
| 1 | Convergence spaces | 1 |
| 1.1 | Preliminaries | 1 |
| 1.2 | Initial and final convergence structures | 4 |
| 1.3 | Special convergence spaces, modifications | 10 |
| 1.4 | Compactness | 21 |
| 1.5 | The continuous convergence structure | 25 |
| 1.6 | Countability properties and sequences in convergence spaces | 42 |
| 1.7 | Sequential convergence structures | 51 |
| 1.8 | Categorical aspects | 57 |
| 2 | Uniform convergence spaces | 59 |
| 2.1 | Generalities on uniform convergence spaces | 59 |
| 2.2 | Initial and final uniform convergence structures | 67 |
| 2.3 | Complete uniform convergence spaces | 69 |
| 2.4 | The Arzela-Ascoli theorem | 71 |
| 2.5 | The uniform convergence structure of a convergence group | 75 |
| 3 | Convergence vector spaces | 79 |
| 3.1 | Convergence groups | 79 |
| 3.2 | Generalities on convergence vector spaces | 85 |
| 3.3 | Initial and final vector space convergence structures | 88 |
| 3.4 | Projective and inductive limits of convergence vector spaces | 96 |
| 3.5 | The locally convex topological modification | 102 |
| 3.6 | Countability axioms for convergence vector spaces | 109 |
| 3.7 | Boundedness | 111 |
| 3.8 | Notes on bornological vector spaces | 116 |
| 4 | Duality | 119 |
| 4.1 | The dual of a convergence vector space | 119 |
| 4.2 | Reflexivity | 125 |
| 4.3 | The dual of a locally convex topological vector space | 131 |
| 4.4 | An application of continuous duality | 148 |
| 4.5 | Notes | 152 |
| 5 | Hahn-Banach extension theorems | 153 |
| 5.1 | General results | 154 |
| 5.2 | Hahn-Banach spaces | 160 |
| 5.3 | Extending to the adherence | 164 |
| 5.4 | Strong Hahn-Banach spaces | 172 |
| 5.5 | An application to partial differential equations | 178 |
| 5.6 | Notes | 181 |
| 6 | The closed graph theorem | 183 |
| 6.1 | Ultracompleteness | 184 |
| 6.2 | The main theorems | 187 |
| 6.3 | An application to web spaces | 192 |
| 7 | The Banach-Steinhaus theorem | 195 |
| 7.1 | Equicontinuous sets | 196 |
| 7.2 | Banach-Steinhaus pairs | 198 |
| 7.3 | The continuity of bilinear mappings | 204 |
| 8 | Duality theory for convergence groups | 207 |
| 8.1 | Reflexivity | 208 |
| 8.2 | Duality for convergence vector spaces | 215 |
| 8.3 | Subgroups and quotient groups | 217 |
| 8.4 | Topological groups | 224 |
| 8.5 | Groups of unimodular continuous functions | 232 |
| 8.6 | c- and co-duality for topological groups | 240 |
| Bibliography | 247 | |
| List of Notations | 257 | |
| Index | 259 |
| Price | Condition | Delivery | Seller | Action |
| $99.99 | Digital |
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Add Convergence Structures and Applications to Functional Analysis, This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional a, Convergence Structures and Applications to Functional Analysis to the inventory that you are selling on WonderClubX
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Add Convergence Structures and Applications to Functional Analysis, This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional a, Convergence Structures and Applications to Functional Analysis to your collection on WonderClub |