Closed Graph Theorems and Webbed Spaces

Cover......Page 1
Title: Closed graph theorems and webbed spaces......Page 2
ISBN 0 273 08403 8......Page 3
Preface......Page 4
Terminology and notations......Page 7
Contents......Page 9
1. MEAGRE SETS AND BAIRE 1 S CATEGORY THEOREM......Page 11
2. THE CLOSED GRAPH THEOREM FOR ~-SPACES......Page 14
3. THE OPEN MAPPING THEOREM......Page 20
Comment......Page 21
2. LINEAR RELATIONS......Page 22
3. THE DOMAIN SPACE......Page 24
4. THE RANGE SPACE......Page 34
1. FAST CONVERGENT SEQUENCES......Page 39
2. BORNOLOGICAL AND ULTRABORNOLOGICAL SPACES......Page 44
1. WEBS......Page 58
Comment......Page 60
2. A TOPOLOGICAL INTERPRETATION......Page 62
3. SOME EXAMPLES......Page 66
4. PERMANENCE PROPERTIES......Page 68
5. CLOSED GRAPH THEOREMS......Page 73
6. LOCALIZATION PROPERTIES......Page 79
1. SPACES OF LINEAR MAPS......Page 86
2. TENSOR PRODUCTS......Page 99
3. SPACES OF VECTOR VALUED FUNCTIONS......Page 102
4• LOCALIZATION PROPERTIES FOR SUBSETS OF L(E,F)......Page 109
1. HOMOMORPHISMS AND DUALITY......Page 113
2. SURJECTIVITY THEOREMS......Page 120
3. LIFTING COMPACT SUBSETS......Page 123
1. SOUSLIN SPACES......Page 136
2. PERMANENCE PROPERTIES AND EXAMPLES......Page 138
3. SOME PROPERTIES OF MEAGRE SET......Page 143
4. THE BOREL GRAPH THEOREM FOR L.C.S.......Page 146
5. THE BOREL GRAPH THEOREM FOR TOPOLOGICAL GROUPS......Page 153
6. FURTHER PERMANENCE PROPERTIES OF SOUSLIN SPACES......Page 155
Bibliography......Page 159
Index......Page 167