Closed Graph Theorems And Webbed Spaces (research Notes In Mathematics)

M. De Wilde. Includes Index. Bibliography: P. 149-156. Cover Title Preface Terminology and notations Contents I. CLOSED GRAPH AND OPEN MAPPING THEOREMS FOR -SPACES 1 Meagre sets and Baire's category theorem 2 The closed graph theorem for -spaces 3 The open mapping theorem II. HEREDITARY PROPERTIES FOR CLOSED GRAPH THEOREMS 1 Introduction 2 Linear relations 3 The domain space 4 The range space III. BORNOLOGICAL AND ULTRABORNOLOGICAL SPACES 1 Fast convergent sequences 2 Bornological and ultrabornological spaces 3·Permanence properties and examples IV. WEBBED SPACES 1 Webs 2 A topological interpretation 3 Some examples 4 Permanences properties 5 Closed graph theorems 6 Localization properties V· WEBS IN SPACES OF LINEAR MAPS 1 Spaces of linear maps 2 Tensor products 3 Spaces of vector valued functions 4 Localization properties for subsets of L(E,F) ·· VI. HOMOMORPHISMS AND WEAK HOMOMORPHISMS 1 Homomorphisms and duality 0 2 Surjectivity theorems 3 Lifting compact subsets VII. SOUSLIN SPACES AND THE BOREL GRAPH. THEOREM OF L. SCHWARTZ 1 Souslin spaces 2 Permanence properties and examples 3 Some properties of meagre sets 4 The Borel graph theorem for l.c.s 5 The Borel graph theorem for topological groups ·· 6 Further permanence properties of Souslin spaces · BIBLIOGRAPHY INDEX