# Best Reference Books – Topological Vector Spaces

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We have compiled the list of Top 10 Best Reference Books on Topological Vector Spaces subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Topological Vector Spaces along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Topological Vector Spaces subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Topological Vector Spaces" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

 1. “Topological Vector Spaces (Graduate Texts in Mathematics)” by H H Schaefer and M P Wolff “Topological Vector Spaces (Graduate Texts in Mathematics)” Book Review: The book is on topological vector spaces. It talks about the familiarity with the elements of general topology and linear algebra. The chapters of the book start with introduction and ends with exercises. The book has examples and counterexamples and has hints where it is needed. It contains new chapter on C^* and W^* algebras.

2. “Topological Vector Spaces I (Grundlehren der mathematischen Wissenschaften)” by D J H Garling and Gottfried Köthe advertisement “Topological Vector Spaces I (Grundlehren der mathematischen Wissenschaften)” Book Review: The book aims to give a systematic account of the most important ideas, methods and results of the theory of topological vector spaces. The book gives the fundamental ideas of general topology. It discusses infinite dimensional linear algebra in detail. Concept of dual pair and linear topologies on vector spaces over arbitrary fields are given in a natural manner. It contains chapters which stress on real and complex topological vector spaces.

3. “Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics)” by Claude Berge “Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics)” Book Review: The book is on set topology, which studies sets in topological spaces and topological vector spaces. The book has a systematic development of the properties of multi-valued functions. It includes topics like families of sets, mappings of one set into another, ordered sets, topological spaces, topological properties of metric spaces, mappings from one topological space into another, mappings of one vector space into another, convex sets and convex functions in the space R” and topological vector spaces. advertisement advertisement

4. “Topological Vector Spaces: Chapters 1–5 (Elements of Mathematics)” by N Bourbaki and H G Eggleston

5. “Counterexamples in Topological Vector Spaces (Lecture Notes in Mathematics)” by S M Khaleelulla

6. “Topological Vector Spaces: The Theory Without Convexity Conditions (Lecture Notes in Mathematics)” by Norbert Adasch and Bruno Ernst

7. “Summer School on Topological Vector Spaces (Lecture Notes in Mathematics)” by L Waelbroeck

8. “Topological Vector Spaces and Algebras (Lecture Notes in Mathematics)” by Lucien Waelbroeck

9. “The Open Mapping and Closed Graph Theorems in Topological Vector Spaces” by Taqdir Husain “The Open Mapping and Closed Graph Theorems in Topological Vector Spaces” Book Review: The book tells about the understanding of three of the deepest results of Functional Analysis, the open-mapping and closed­ graph theorems, and the so-called Krein-~mulian theorem. It contains important notions and well known results about topological and vector spaces. The book presents the material to give a quick resume of the result and the ideas that are commonly used in the field. It contains a detailed study of the open-mapping and closed-graph theorems as well as the Krein-~mulian theorem.

10. “Topological Vector Spaces II: 2 (Grundlehren der mathematischen Wissenschaften)” by Gottfried Köthe