TY - BOOK AU - Bourbaki,Nicolas TI - Topological vector spaces: chapters 1-5 T2 - Elements of mathematics SN - 9783540423386 PY - 1987/// CY - Berlin PB - Springer-Verlag KW - Linear topological spaces KW - Functional analysis KW - approximation KW - topological vector space N1 - Translation of: Espaces vectoriels topologiques; Includes indexes; Bibliography: v. 1, p. [346] N2 - This [second edition] is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. Table of Contents. Chapter I: Topological vector spaces over a valued field. Chapter II: Convex sets and locally convex spaces. Chapter III: Spaces of continuous linear mappings. Chapter IV: Duality in topological vector spaces. Chapter V: Hilbert spaces (elementary theory) ER -