Topological Vector Spaces Chapters 15 [Paperback]

This is a softcover reprint of the 1987 English translation of the second edition of Bourbaki's Espaces Vectoriels Topologiques. Much 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, reflecting decades of progress in the field.

I.  Topological vector spaces over a valued division ring I..- ? 1. Topological vector spaces.- 1. Definition of a topological vector space.- 2. Normed spaces on a valued division ring.- 3. Vector subspaces and quotient spaces of a topological vector space; products of topological vector spaces; topological direct sums of subspaces.- 4. Uniform structure and completion of a topological vector space.- 5. Neighbourhoods of the origin in a topological vector space over a valued division ring.- 6. Criteria of continuity and equicontinuity.- 7. Initial topologies of vector spaces.- ? 2. Linear varieties in a topological vector space.- 1. Theclosure of a linear variety.- 2. Lines and closed hyperplanes.- 3. Vector subspaces of finite dimension.- 4. Locally compact topological vector spaces.- ? 3. Metrisable topological vector spaces.- 1. Neighbourhoods of 0 in a metrisable topological vector space.- 2. Properties of metrisable vector spaces.- 3. Continuous linear functions in a metrisable vector space.- Exercises of ? 1.- Exercises of ? 2.- Exercises of ? 3.- II.  Convex sets and locally convex spaces II..- ? 1. Semi-norms.- 1. Definition of semi-norms.- 2. Topologies defined by semi-norms.- 3. Semi-norms in quotient spaces and in product spaces.- 4. Equicontinuity criteria of multilinear mappings for topologies defined by semi-norms.- ? 2. Convex sets.- 1. Definition of a convex set.- 2. Intersections of convex sets. Products of convex sets.- 3. Convex envelope of a set.- 4. Convex cones.- 5. Ordered vector spaces.- 6. Convex cones in topological vector spaces.- 7. Topologies on ordered vector spaces.- 8. Convex functls