Koethe G. Topological vector spaces

Köthe, G. Topological vector spaces I. (English)
[B]Berlin-Heidelberg-New York: Springer Verlag 1969. XV, 456 p. (1969)Классический учебник по теории топологических векторных пространств, написанный одним из создателей этой науки. Содержит следующие разделы: Chapter One "Fundamentals of General Topology" (Topological spaces, Nets and filters, Compact spaces and sets, Metric spaces, Uniform spaces, Real functions on topological spaces). Chapter Two "Vector Spaces over General Fields" (Vector spaces, Linear mappings and matrices , The algebraic dual space. Tensor products, Linearly topologized spaces, The theory of equations in E and E*, Locally linearly compact spaces, The linear strong topology). Chapter Three "Topological Vector Spaces" (Normed spaces, Topological vector spaces, Convex sets, The separation of convex sets. The Hahn-Banach theorem). Chapter Four "Locally Convex Spaces. Fundamentals" (The definition and simplest properties of locally convex spaces, Locally convex hulls and kernels, inductive and projective limits of locally convex spaces, Duality, The different topologies on a locally convex space, The determination of various dual spaces and their topologies). Chapter Five "Topological and Geometrical Properties of Locally Convex Spaces" (The bidual space. Semi-reflexivity and reflexivity, Some results on compact and on convex sets, Extreme points and extreme rays of convex sets, Metric properties of normed spaces). Chapter Six "Some Special Classes of Locally Convex Spaces" (Barrelled spaces and Montel spaces, Bomological spaces, (F)-and (DF)-spaces, Perfect spaces, Counterexamples).