Linear Topological Spaces is a comprehensive book on the theory of topological vector spaces, written by John L. Kelley. The book covers a wide range of topics including the basic concepts of topology, linear algebra, and functional analysis. It provides a rigorous treatment of the subject matter, with detailed proofs and examples. The book begins with a discussion of topological spaces and their properties, followed by a detailed study of linear algebra and its applications in topological vector spaces. It then moves on to cover the theory of Banach spaces and Hilbert spaces, as well as the theory of dual spaces and the Hahn-Banach theorem. The book also covers the theory of locally convex spaces and the topological properties of linear operators. The book is written in a clear and concise style, making it accessible to both graduate students and researchers in mathematics and physics.Additional Contributors Are W. F. Donoghue, Jr., Kenneth R. Lucas. B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, And Kennan T. Smith.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.